Every now and then after a big rain these crop up in my basement. No obvious cracks or anything where they pop out of the unfinished concrete floor. I try to dispose of them without too much opportunity to shake of spores, and then douse the floor with bleach, but I also admire their ability to grow with no apparent nutrients.
If it's the same kind of tree then definitely. A new tree can graft to the old root system and revive it which keeps the mushrooms alive even though the tree would normally be too immature to support that specific fungal partner.
I'm curious if you know what kind of tree it is, the bolete looks a bit like Suillus which tend to be really specific about their partner. If you're in the Pacific Northwest region I could probably figure out the species from the tree.