It should be possible to get a tame player monster, but only from a bones level: you would need to tame the ghost of the former player and use undead turning to draw it back into its body. The tameness of the ghost would then be reflected in the player monster being tame.

When a player is killed by a giant spider and leaves bones, there will be a web trap placed on their square, and occasionally one or two giant spider eggs.

Bones of tortle players contain a tortle shell, which is useless except as an indicator the dead player was a tortle, or as polyfodder.

Items in a bones pile, in addition to being cursed, could be subject to additional degradation such as erosion, loss of magical charges, or blanking. (Though since a new player will arrive in the bones level apparently immediately after the death, it could be a bit of a stretch to have the items degrade so much.)

Internally mark all of your starting gear with a special flag; if you die before receiving the quest, any items marked with this flag get degraded when placed into your bones pile: things like magical armor becoming nonmagical, wands lose charges, scrolls may fade, and spellbooks are made too faint to read more than once.