They search the buildings encouraging more following than he thought was possible. Some of the braver refugees go then further still and bring back their own groups with them.
Fëanor is aware that the time is running out. Another group of goblins can appear any minute and there will be a moment when the attackers realise - dumb as they are, they have already shown they can adapt - that their initial plan to just randomly wreck havoc among hapless civilians stopped working and take more aggresive measures.
The city may look deserted but the sole fact there are people coming of hiding still is a proof it's far from it.

"We may need to go from house to house," he notes to Curufin as they send another group up "as far as we can from the start of the path."

The way up the cliffside is by no mean safe. There are wild animals on the road and a couple of stray goblins may venture there. Yet it's far safer than staying down here and they can't be in two places at once. And the rest of the Orange team is either at the very top directing the refugees further to the fortress or somewhere along the way. So that part of escape route is taken care of.

Yet all this will be in vain if the entrance gets overrun by goblins. They have to keep it open even if that means setting camp for the night here.