I'm pretty sure it works like that just as company pensions used to work. Typically that may have been 7.5% salary and 7.5% from the company. Large ones tended to be over subscribed over time so that and more investment in property changed to 7.5% from salary only. Often called a pension holiday which sometimes doesn't work out well for the people in it. A pretty usual set up was 40years contributions for 60% final salary. Mine worked out differently as it was moved around when I was sold - twice . It resulted in a pot to purchase an annuity.
Not checked Police but with others the pensions are paid from a fund that has been built up since their inception. Terms vary across the civil service. Teachers for instance get a cash payment as well. Some I believe are index linked some I think aren't.
The company ones were set up such that the fund belongs to the company not the members. That can mean under certain circumstances they can raid it. Not sure how that works out with civil service type jobs but they appear to merge funds from time to time.