Can using a bad tube hurt an amplifier?

Yes and no. The tube can just fail and stop working with no other symptoms, or it can fail and cause a fuse to blow, or burn up a resistor, or destroy an output transformer. It depends on the amp. For what it's worth there are millions of tubes and tube amps in use and no major incidents.

It can cause serious damage ,  I wouldn't risk using a tube if zi suspected it was bad. 

Tube amps will use either an automatic  bias scheme where the amp will maintain the bias voltage for the tube or is is manually biased periodically by means of an LED , built in meter or multimeter.   

If you suspect it's a bad  tube, replace it.    Usually a bad tube will just blow a fuse or take out a bias resistor  ut it can cause catastrophic damage. 

@emergingsoul 

Which tube amp do you own or are considering purchasing?

When you mention "and then voltage changes over time gradually" are you referring to tubes going out of bias or actual voltage changes from the power grid?  If the former, it is imperative that a tube amp be easy to bias or self-biasing, which most newer offerings are.  

A bad tube can definitely damage an amp or preamp.

and speakers....they can damage those too. I always use a broom handle when I'm turning on my tube amps...

Yes if you're lucky just a blown fuse and possibly blown resistor but as stated above things can get much worse.

Anyone who has ever seen a tube arc internally knows it's a pretty scary fireworks show. 

If the bias runs away you'll often see the plates turn a red orange , "Red Plating"     Definitely get an amp checked out if this happens with an auto bias amp or if it happens on a manual bias amp that won't hold its bias.   Lethal voltages inside,  have someone familiar with tube amps check it if it's not as simple as bad tube .

Sounds like voltage changes if they occur from a tube should be corrected by the auto bias?  

Yes, I just had this happen to me: everything working fine for 4 months with the 300b Gold Lion’s in my Coincident Frankenstein stereo amp. The amp and tubes are both 4 months old, I haven’t touched anything in weeks, and I turn it on a few weeks ago and one 300b tube is much brighter than the other one. By the time I got to turn it off I hear sizzling bacon, I shut it down and witness what appears to be plenty of smoke bellowing from the amp. Israel Blume Coincident owner says the tube has "run away" which I believe is the same as "red plating" as stated above. I have no way to check tubes so I sent if off to the retailer and they have checked it and confirmed it is bad, warrantied it, and a replacement tube is on the way back. There is a 1% failure rate and I am one of the lucky ones.

There is automatic bias circuit in this amp so nothing to adjust on my end, but no special protection circuit to shut off the amp in the case of a faulty tube, not sure how many amps have this? 

No warranty for the amp as it was the tubes fault. Easy fix though thanks to point to point circuit wiring. 

The joys of tube amps I suppose. 

  I had this happen about 5-6 years ago with my Had Inspire SEP amp. It’s auto bias for the two power tubes and also will take multiple value rectifier tubes allowing me to raise or lower the voltage. It takes EL-34 to KT-150 and I can run any combo of power and rectifier tube. I had a new pair of GL KT-77’s that were at approximately 100 hours. I heard a loud pop from the amp and a really loud bang from my left speaker. I immediately hit the power switch and saw a wisp of smoke coming from inside the chassis. The tube never changed appearance when this happened and the left channel went dead. I took off the bottom plate and discovered the entire internals were coated with paper, oil and foil from the explosion. Also a large resistor exploded and together they generated enough force to break the terminal strip that the circuit was attached to. I shipped it to Dennis for repair and included the two power tubes for him to test. He confirmed that I had a “ Run Away “ tube. The vendor refunded the tubes and I paid for the damage. Another time I had a 6550 tube pop due to the glass envelope failing. I heard the sound and turned off the amp. The tube had a fracture that ran top to bottom and was completely white on the inside of the glass. There was zero damage to the amp, and I just replaced the one tube. Shit Happens when you run tubes, it’s part of the lifestyle. Cheers , Mike B. 

The problem I had was the tubes were fine for several months.  And then one day within 20 minutes one of the tubes started over heating and glowing alot more  it wasn’t the glowing tube that was the problem it was another tube in the same series, since they’re all connected.  all the tubes test fine it’s just that one of the tubes begin having voltage problems after 20 minutes. Very difficult to diagnose when you have many tubes.

There’s no way to predict this.  These were NOS tubes, presumably supposed to be higher quality than the new stuff.

I feel your pain. I was recently gifted a pair of Rogue M-180’s with one needing repair. But I still wanted to see what happened. I changed tubes , tried different things and two things would happen. One was a horrible super loud droning that I feared would blow my speaker. The other thing that happened was the music would play with a very very slight harmonic distortion. Also turning the amp off caused noise. I shipped them both to Rogue for diagnosis and repair. The issue was a single resistor in the circuit of the single 12AX7 phase tube. However I was told that the bridge rectifiers in both amps were weak and I should repair. My solution was to spring for the $2500 Dark Upgrade and then get 8 new power tubes and 6  new NOS signal tubes, 3 for each amp. I have $2500 for the upgrade which included new Vishay resistors , Hex Fred diodes new larger capacitors , some wiring and Cardas speaker terminals. With tubes and shipping I’m at $4K for my free amps. It’s always something, and I wish we had a local tech. Yes we suffer reliably issues, tube issues and the jabs from the SS crowd and now the class D crowd. And I’m happy right in the middle of my domain. Stay strong brother , and I’ll meet on the Road To Happy Destiny, or at least Tube Addicts Anonymous. Much Respect , Mike B. 

@buellrider97 

Yes we suffer reliably issues, tube issues and the jabs from the SS crowd and now the class D crowd. 

but those other amps are not bulletproof, I might argue they are no more reliable than tube amps. I wouldn't say I was an early adopter for class D amps, but both the Nord's I bought about ten years ago with the Hypex smps1200a400 power supplies lasted exactly 4 years before they expired. They have since revised them, with elimination of one prone to fail capacitor- not sure if they last longer now. 

I have also had issues with Mcintosh amps. Nothing lasts forever. 

Is it -1 for tubes or +1 for SS? Who’s keeping score?

When you have red plating with tube amps until one measures plate voltages you won't know for sure if its tube failure or amp issue, you may be damaging more tubes if amp is the issue. Tubes going bad without red plating likely lost vacuum, sometimes this seen as interior of tube enveloped in blue haze, other times not, another sign is white getter.

Just had Fedex drop off the replacement Gold Lion 300b, inserted it in the amp, and voila, music is playing again. 

Just one $5 220uf Rubycon capacitor was all that needed replacing. 

Lucky the cap went first, and not after various other parts as in this component:

https://www.youtube.com/watch?v=ZaEiO_9qMwY

@kennyc +1

My 1948 Capehart has a main power supply in which the xmfr winding for the rectifier tubes is fused to prevent catastrophe.