Garner 9 abstensions, so to speak? Just let the case carry over to the next court after someone retires or some vacancy is filled?
Nine abstentions? Highly unlikely.
But what does happen, regularly, is that cases are DIGged – shorthand for “Dismissed as Improvidently Granted.” This occurs when four justices have voted to grant certiorari, and then for some reason a consensus arises among the justices that “we should not hear this case.” In such a situation, it’s as though they’d refused certiorari in the first place – the lower court decision (highest state court or, usually, Federal Appeals Court) stands as law for the area it has jurisdiction over.
The justices decide which cases they want to hear, so it’s unlikely that they would vote to hear a case but then express no interest in resolving it.
Occasionally, when a seat is unfilled (say, after the death or resignation of a justice and before his successor is appointed), the court will end up with a 4-4 vote on a case. In that case, the lower court ruling stands.
More often, they set it for reargument after the new justice has been appointed and confirmed, effectively with him having the tie-breaking vote. The 4-4 vote resulting in the lower court ruling standing (but without precedential value outside the jurisdiction of the lower court) happens when there is a full court but one justice recuses himself because, e.g., he has a financial interest in one of the companies involved in the suit, he prosecuted the case while Attorney General, etc.
In criminal cases, there’s also the possibility of the death of the accused before the Court renders its decision. In that case, the appeal abates. (This happened a few years ago with the Ken Lay case, although in that case it was at the Federal Court of Appeals level, not the Supreme Court.)