Excellent question.
Simple answer is it seems that most do not.
In Australia the regulators require them all to keep all customer balances in segregated bank accounts. However a recent failure by one in the Australian Capital Territory revealed that it hadn't been happening and the regulator had failed miserably to police the law. Hopefully the regulators in the other states and territories are doing a better job of it.
I understand that the UK books operate under similar laws.
Betfair certainly does. I have been assured that Pinnacle and Matchbook do also.
SBR puts out ratings on books but appears to have no clue on this issue. They don't even attempt to assess a book's financial stability and ensure that player funds are segregated.
If you detect a book which is slow paying or limiting withdrawals you have very probably found one which hasn't got the funds to pay all players.