Two live centers?

[AHill]

Using a forstner bit in a head stock or tail stock will drill into the wood not hold the wood with any pressure put  on them.  I do not know how you can keep from doing that.

Maybe.  If the tailstock has a live center, the Forstner bit will merely rotate the workpiece.  A drill only works as a drill when the workpiece is stationary.  Think about when you're using a drill press and holding the workpiece with your left hand while plunging the drill with your right hand.  If you lose grip on the workpiece, it just starts spinning around.

It's possible that if your gouge (or skew or whatever) applies too much pressure against the workpiece on your lathe, the Forstner bit could start to drill, but it'll never go deeper than how deep you've set the flutes into the workpiece.