The ability is granted as part of the copy effect, which means it will be removed by any effects that would remove abilities regardless of when the effect was created.
01-08-2008
wotc
If an Unstable Shapeshifter is on the battlefield when another Unstable Shapeshifter enters, the first one gets the second one's triggered ability, so it will copy the next creature that enters twice. It will only do so the next time a creature enters, because the second "becomes a copy" effect to resolve will erase the extra triggered ability.
04-10-2004
wotc
When it changes "shape" to a new creature, any "enters" abilities of the creature do not trigger.
04-10-2004
wotc
If a creature enters that has some characteristic or ability set when it enters, the copy does not get to make that choice (because it is not entering. All values are zero and all checks for choices consider the choice not to have been made.
04-10-2004
wotc
If the creature has power/toughness that is continuously recalculated, so does this copy of it.
04-10-2004
wotc
The copy effect is not targeted.
Random a card of Magic: The Gathering (MTG), but you can also roll the D20 dice, random a Planeswalker, have fun with the random rules and more.