At my previous bank (employer) we could be over or short a cumulative total of $2 every month before there was any disciplinary action. Techinically, I could be short $10 one day, over $8 another, over 50 cents another, short 10 cents, over $6, etc. as long as the cumulative total was no more than $2 in that month. However, they also had the good sense to look at the number of times someone was over or short. More than twice in a month and you were likely to be audited by your head teller or manager once or twice a week for a month or more.
At this bank, there is no set policy, which makes me a little crazy. I think it opens us up to potential legal problems. (“You fired me for being short $10 but didn’t fire Suzie when she was over and short all the time but it’s all because she’s the manager’s pet!”)
On the occasions I go to a branch to help out, I count whatever drawer I am given to make sure that it matches the previous balance. Then, and only then, do I accept responsibility for it. At the end of that day, any mistakes are on me, not on whoever used the drawer previously.
One time I can see a problem that isn’t necesarily the cashier or teller’s fault is when opening a roll of coin. If it was rolled by a customer and not verified before accepting it, it may be over or short. And I could tell you some stories about that. But I won’t.