No. Un less it's resprouted from the stump, there's nothing to provice food and keep the roots alive.

You are seeing some other plant's roots.

Keep in mind that a tree's roots usually grow far beyond its canopy. So you might consider other nearby trees. Rough estimates of the size or tree root systems include 1. a radius of at least 2 to 3 times the radius of the dripline and 2. a radius of 1.5 times the tree's height or more.

I am originally from the west coast near the red wood forest. Yes, a cut off root knot can produce new trees. In fact you can buy these knots from trees of mystery. If the roots you are speaking of are getting enough water to remain moist year round it will continue to grow in an effort to grow a tree again. My suggestion is to allow your rose bed to dry out a bit... or move them to a different location and allow the bed to dry out to hard earth state.

Sprouting a new tree is an entirely different thing than roots actively growing for 15 years without food!!!!