Yes, filter caps go bad when gear is not used for a very long time because electrolyte "eats" out aluminium oxide, a dielectric, reducing breakdown voltage (presence of voltage slowly rebuilds it), but filter caps can also go bad because they simply dry out. Current heats up dry capacitor because of its increased ESR causing further increase of ESR with temperature, resulting in avalanche effect and explosion of the capacitor. Because of that electrolytic caps have either fuse (rubber plug) or weakened top (groves). In room temperature capacitor will last 40-50 years but every 10degC temperature increase cuts its life by two. Capacitors placed in hot areas, for instance close to tubes, won't last very long.
Safety of Older Electronics
Some electronics never die. They just get moved to secondary, tertiary, etc. systems. In my case, I have two old receivers connected to televisions. I'm guessing one is 25 and the other 30 years old. The remote sensors are on all the time and occasionally one forgets to turn the receivers off. They can be replaced with relatively inexpensive amplifiers for how they're used, but I thought if it ain't broke don't fix it. At least until recently when I've started to wonder if continuing to use them is a smart idea even though there is nothing apparently wrong with them. I'm thinking in terms of a damaging (catastrophic?) failure particularly when the receiver is unattended. I'd appreciate input whether one should continue to use older equipment that can be inexpensively replaced.