If the revealed card isn’t a creature card, it stays on top of that player’s library. Shapeshifter’s Marrow remains an enchantment.

If the revealed card is a creature card, Shapeshifter’s Marrow becomes a copy of that card permanently. It’s no longer an enchantment.

In a Two-Headed Giant game, this ability triggers separately for each player at the start of the opposing team’s turn. If the first ability to resolve reveals a creature card, Shapeshifter’s Marrow becomes a creature. If the second ability to resolve also reveals a creature card, the ex-Shapeshifter’s Marrow then becomes a copy of that creature.