The simple answer is that the "completed" project is ongoing. Much as a motorway doesn't stop emitting once it's completed, a landfill gas capture system does not stop reducing emissions once construction is complete, and a forest doesn't stop absorbing carbon once it's planted.
But the exact answer is generally in the fine print. Often those projects are front-loaded, there's an estimate made of how much carbon will be avoided/absorbed during the entrie working life of the project and those negative emissions are sold on day one, then the project is complete. That's where a lot of the scams come from - the originators have essentially sold promises, and once they're paid they lose interest. So you need to do quite specific research to find out the exact details for the scheme/scam you're buying into.
There are other traps, forsts can burn, machinery can irrecoverably break down, wars can break out. In those cases even the best intentions can fail, and often the insurance payout only covers the money cost, there's no provision for "net zero emissions replacement" to allow the original abatement to take place. The PV system on my roof, to use a trivial example, was funded by selling the "expected lifetime output" but it was impossible to buy insurance that did not also include selling the lifetime output of the replacement system (viz, it covered the cost of a new, equivalent system but not buying back the lost non-emissions of the system it replaced).