Why you were shutdown can affect your resurrection. 1) credit line, and 2) how willing Chase is to let you open a second card (assuming your Ink card stays open.) For example, if you were shutdown for suspected bust-out fraud, then Chase may be stingy with credit line and downright apoplectic at giving you another card anytime soon. If however the shutdown was for something lesser, say, manufactured spend, then you might be better off.

RNE, opining that Chase's labyrinthine policies are a mystery to everyone -- even Theseus.