When a copy of a creature with the undying ability dies, the undying ability will trigger and return it to play. This is due to the last known information when the card was in play, which is what leaves-the-battlefield abilities (like undying) look for to determine whether they should trigger. When it returns to the battlefield, it will be a new object with the +1/+1 counter on it, and you choose something to copy at that time.
For example, if your Phantasmal Image is a copy of Geralf’s Messenger and it dies (without any counters on it), it will be returned to the battlefield with a +1/+1 counter, and you may choose something to copy. If the original Geralf’s Messenger is no longer in play, you can’t have the image enter as a copy of that, even though it was one when it died. If you can’t or choose not to copy something else, the Image will just enter as a 1/1 creature (because of the +1/+1 counter), and it won’t have the “Sacrifice me when I’m targeted” ability (that ability is only added as part of the copy effect). So if you ever see a Phantasmal Image on the battlefield with a sword equipped to it, that’s probably how it happened.
Today’s Rules Tip suggestion submitted via the “Suggest a Rules Tip” form by Ryan Porter