Using Tape Out from Preamp for powered sub woofer.

Although you can control the sub volume with it’s own volume control, you will have to adjust this every time you change your main volume. The sub volume control is mainly to adjust the "relative" volume levels, and once adjusted, usually is left alone. Tape monitor outputs are fixed and do not respond to main volume levels.

I would avoid line level splitters at all costs.

Most subs have a high level speaker input as well as a low level line input. I would use these tee’d off the main speaker outputs. Much better than a line level splitter IMHO.

Another trick I have used is a isolation transformer connected off the main speaker outputs. The transformer isolates the output speaker levels and reduces the level to line level for the sub. The product I have used is called the "ZDirect" made by ART. It has two -20 dB attenuators and an isolation transformer, so it can reduce speaker voltage levels to line input levels easily.

You may also be able to use a quality Y-connector at the end of your IC cable from your preamp output (not tape out) to your amp. So, run a second IC from the Y-connector to your sub(s). This will allow your preamp to control the volume, but you should still be able to adjust the gain control on your sub(s) when playing at low volume.
Kenny

As long as you don't mind adjusting the volume on the sub, I see no issue. Try it and see starting off at the lowestvsetting on both pre and sub.

Noromance, your question is correct. 
To clarify my point further, I do have volume control on my powered Sub.  And I need more bass when I'm playing music at lower volume, which is the case most of the time. And as I increase volume from preamp the bass from the sub is too much for my taste. And I hate to standup every time to reduce bass level on the sub. So I want to bypass the preamp volume control for subwoofer. I would like to try this arrangement, but just want to make sure it's technically correct and will not damage preamp or the Sub. 

Couldn't the OP use tape out and control the volume from the sub as he/she wants different levels depending on volume?

It's not a stupid question, but you cannot use it for a sub. :)

The problem with the Tape Out loop is that the volume control doesn't control the level so your sub will always play at maximum.

Better to get a Y splitter, or use the speaker level inputs on the sub, if available.

Best,

Erik