A creature without a text box can later gain abilities. Those abilities will work.

If anything cares about Phoebe's rules text, flavor text, or watermarks, consider all of her text boxes as if they were one. If anything cares about the rules text, flavor text, or watermarks of a creature whose text box was stolen, the effect sees nothing.

If Phoebe steals a creature's text box, that creature no longer has that text box. Phoebe now has her own text box in addition to the one she stole.

If Phoebe leaves the battlefield, the stolen text boxes are lost. She doesn't keep them, and she certainly doesn't give them back to their original owners.

If Phoebe has abilities that contradict one another, the most recently added one wins. For example, if Phoebe has the text boxes of both Beast of Burden (power and toughness equal to the number of creatures on the battlefield) and Psychosis Crawler (power and toughness equal to the number of cards in your hand). Phoebe's power and toughness would be defined by the text box added most recently.

If a creature loses its text box, leaves the battlefield, and then returns to the battlefield, it will once again have its text box. This won't affect Phoebe, who presumably still has the one she stole from the original creature.

If Phoebe steals a creature's text box, that creature will no longer have flavor text and can then block Phoebe.