In Deathly Hallows we learn that Dumbledore asked Snape to keep an eye on Quirrell. We presume because he thought Quirrell was fishy.
Keep an eye on Quirrell, won't you?
I assume at some point after that exchange after that point in Philosopher's Stone, Snape was talking to Quirrell about the protection of the stone in the Forbidden Forest, presumably conversing on how to get past all the protection.... (Snape might have traded info with Quirrell.)
"... d-don't know why you wanted t-t-to meet here of all p-places, Severus..."
"Oh, I thought we'd keep this private," said Snape, his voice icy. "Students aren't supposed to know about the Sorcerer's Stone, after all."
Harry leaned forward. Quirrell was mumbling something. Snape interrupted him.
"Have you found out how to get past that beast of Hagrid's yet?"
"B-b-but Severus, I --"
"You don't want me as your enemy, Quirrell," said Snape, taking a step toward him.
"I-I don't know what you
"You know perfectly well what I mean."
An owl hooted loudly, and Harry nearly fell out of the tree. He steadied himself in time to hear Snape say, "-- your little bit of hocus-pocus. I'm waiting."
"B-but I d-d-don't --"
"Very well," Snape cut in. "We'll have another little chat soon, when you've had time to think things over and decided where your loyalties lie."
So obviously Snape (playing double agent as always) and therefore Dumbledore knew it was just a matter of time before Quirrell attempted to steal the stone, did Snape and Dumbledore have a backup plan, as I doubt they planned that the golden Trio was going to save the day.