Dear Ceals and Natasha,
It is functionally impossible, in a busy building, to completely prevent people from coming in, though all hirers - and indeed all Quakers who have a fob, too - sign an agreement pledging not to leave the outside doors propped open or unattended, and not to let anyone in who is not their personal guest. When people break this agreement (and they do), one of the things I emphasise is how it puts the lone workers we have here at risk. Leaving the door propped open and unattended also gets them a very firm talk about how flouting the Ts&Cs could put their continued hire at risk.
We're a bit of a warren, with many of our rooms having two ways to enter or leave, and we are in a very busy part of town. We do have resident volunteers, and one of their tasks every night after the last of the hirers have left is to do a walk-around of the building, opening every door that isn't locked (including in the non-public areas of the building), to make sure someone hasn't squirrelled themselves away, and to make sure that the doors to the street are properly closed. Our cleaner works overnight, in the small hours, and he also checks the building as he works his way around.
The one time in the last seven years that this happened, it was discovered by a hirer opening the door of her hired room in the basement, to find someone sleeping across the doorway. I signposted this person to a range of appropriate local services (which the Meeting supports), and we continued to welcome him to worship, etc, until he found what he was looking for and moved on. We've had our fair share of characters come through the building, and in many ways it's amazing that there hasn't been more of an issue, bearing in mind the area we are in includes a lot of very vulnerable people.
When we have had thefts (eg of handbags, or our portable projector), it's happened at the same time as Meeting for Worship, when our front door is open (as the doorkeeper's purpose is to welcome people in, not keep them out!), so I don't think there's much that can be done about that apart from to remind people to take care of their belongings, as it's easy to relax in the Meeting House and think there's no risk at all.
As for a formal policy on what to do when we've had people come in when they shouldn't: normally I'm the one called to manage the situation, but we don't have a policy as such. Perhaps we should, so I'm grateful that you raised this.