Can payroll jobs go to the Last Friday/Working day etc?

Yes.

Your payroll workflow system can have as many trigger fields as needed. You can supplement your normal weekly, monthly etc trigger fields with some special options. This includes rolling forward to the last working day of the month and also to the Last Monday, Tuesday, Wednesday, Thursday and Friday.

You can read here how to set up a new trigger field, including with these options.

In addition you may want to check your monthly payroll trigger as there is an option that treats the 28th as a normal day (rolls forward to the next 28th) and an option to treat it as the last day of the month (rolls forward to end of next month).