No, if Billups or Arenas would refuse to report to the team that claimed them, or to retire, they would forefeit all the money they are owed, not just the portion the new team would pay them.
If Billups wanted to be able to choose which team he'll play for this season, all he had to do is go to the Knicks and ask to be released from the final year of his contract before they waived him. They would have been more than happy to oblige. Then he could go sign with Miami for the minimum. But no, he wants to get paid the $14M he is owed by NY and still be able to sign with Miami or another contender. The rules of the new CBA make that more difficult than in the past due to the modified waiver system, so now in order to force the issue he is threatening any team that may think of claiming him that he will cause problems for them if claimed.