I haven't found that to be the case typically -- you could always serialize some information into the task to check for things like this.

Also consider if the machine running that process just disappears and that process dies. Putting work into a task queue allows you to do it durably until it can be processed so that it's not lost in some typical "that machine/instance died" scenario.

This might not be viable all the time, what if you have a stream of tasks being put to the queue ? The alternative would be to ensure that any change in the job contracts are backward compatible, and if any change in contract would need to have a remediation/migration plan for handling pending tasks.