AP
In the 8-K form Twitter filed to announce Costolo's exit, the company writes that he also agreed to cancel all of his remaining unvested equity until after July 1 2015, which is when his departure becomes effective.
Here's what the document says (emphasis is our own):
In consideration of your continued service as Chief Executive Officer through the Employment End Date, you will continue to vest in all Company equity awards held by you and outstanding as of the date hereof through and including the Employment End Date. Following the Employment End Date, all Company equity awards that remain unvested as of that date shall cease to vest and will be cancelled and unvested shares forfeited. The terms and conditions of your vested Company equity awards as of that date and the governing plan(s) shall remain in effect as set out in those documents.
In an earlier filing, the company noted that Costolo was in an "at-will" employment arrangement, where either he or Twitter could end his employment unilaterally.
Jack Dorsey, one of Twitter's co-founders who is taking over as Twitter's interim CEO, will also remain as the CEO of Square while Twitter searches for a new permanent leader.
Dorsey isn't accepting any pay for his role as the interim CEO of Twitter.