My first job out of college back in the mid-90s was processing expense statements for a small government contract (~200 employees). We were a division of a large corporation and would handle all our employee expense statements within our division. The first rule (and this applies across the board) was that for the most part employees could be trusted. So I was mainly looking for unapproved expenses (in this case anything over $100 had to be approved by their direct manager, anything over $500 had to be approved by their group manager, and anything over $1000 had to have division manager approval). While I was scanning I was just double checking to make sure they didn't have some random expense listed (i.e. cash advance on the credit card). After that it was fairly simple. The employees all had company credit cards that had personal guarantees to the employee, so if the payment wasn't made the employee was ultimately responsible for the bill. The only thing the company did was allow employees who may not otherwise qualify for the card eligible. Whenever an employee was ready they would fill out an expense statement and submit it to me with all their receipts. I would process everything and take it to the division head for final approval. The next pay period the expenses were included in their check (pre-tax).
My second example was with an Internet startup. I was employee 24 and when I first started it was pretty much a free for all on company expenses. There were no real controls in place, however, as time went on and we grew similar controls were established like above. Approvals were required at certain cost triggers. And expense statements were submitted for final approval. Again, we had company credit cards that were personally guaranteed but backed by the company.
Finally, when I worked at Microsoft in the late 90s/early 2000 the experience was very similar to both the above. There were thresholds for expense approvals, we would fill out expense statements online that went to our manager for approval and I can't remember if we got a separate checks or if they were included in our check. Like the other two examples, expenses started at the team level and moved up the chain depending on what the threshold was.
In all the cases there were clear policies in place regarding what was an expense and what was not. It was clear that if an expense wasn't approved the employee was responsible. And there was always someone reviewing the expenses to make sure they were acceptable. While time consuming, it is really not a complicated process and a single person can process expenses for a larger group (in my first case I personally manually handled - pre-Internet - about 100 expense statements a week). Unless there it is a company requiring extensive travel for all employees there really should not be a lot of direct "employee expense" statements.
After a while that, and a few other things, got a bit out of hand.
Rather than just go after that, we've made it a goal (among other quarterly goals) for everyone to work towards a certain amount of profitability that people can have a part of.
In addition to reducing expenses (yes, it's cheaper) it's also created a bit more of a frugal culture in the company. It's great, people watch what they spend themselves and are much more concerned about their departments' budgets.
Mind you, we have less than 30 employees at the company (I'm one of the founders).
Also, all expenses automatically go to your manager and then get reconciled by our accountant who basically has OCD and will question anything that even looks remotely questionable to anyone including management.
Point is, we created this more frugal culture so everyone can have a bit more in the long run.
For the most part though employees were not upset by the transition from spending freely to frugal. I learned from my first job doing expenses that the majority of employees, given simple controls/policies, will abide by them. Some may push the limit from time to time, but blatant expense fraud can be overcome, in most cases, with minimal time/effort and some basic oversight. Having a system of checks/balances (thresholds and management approval limits) along with a final accounting review prior to reimbursement prevents most cases.