Until the well is shut in. That will happen when they are able to put another preventer on the wellhead, either before or after the relief wells are finished.
Depending on what the determination is as to the stability of the wellbore, they will either P&A it, or drill out the cement in the production casing and complete the well. Either way, I suspect that they are going to have to remove the original BOP at some point. That'll be fun.
Not too bad, really. If the well is under control (think heavy mud, relief well,) they can set a plug or two and if there is a decent cenent job around the casing, they'll be good to go. People nipple down BOPs on a regular basis and move them to the next well while production equipment is installed on the wellhead. A workover rig can drill out the plug after the BOP has been replaced (with production pressure control equipment).