I recently purchased a house. As part of the process, I needed to apply for a mortgage. The bank wanted a statement from my employer about my income from them, along with my last 2 complete years tax documents.
The bank had an inquiry. My employer had said my salary + bonus was X, but in the first of these two years, my tax documents said my income from my employer that year was 2.5X. The extra 1.5X was due to the employer being bought out and some change of control terms in the RSUs causing immediate payout of what would normally have been paid out over 4 years. Since I kept the documents of the RSU terms and the payslips, I could provide these to the bank to clear the matter up.
Notably, had I not kept my own copy of these documents, I could not have gone back to my employer for new copies. Due to the change of control, they had changed payroll vendors, and had eventually terminated the contract with the old vendor, so I could not have gotten a payslip from 1.5 years ago. Similarly, in the move to the new owner's HR system, the company had lost many of their records of agreements with employee's, including contracts etc., so it's not clear they would still have the terms of the RSUs, especially since the change of control payout rendered this a "completed" transaction. And later events made it clear that they did not have, e.g. a copy of my employment contract.
Similarly, if I ever had had a dispute over the terms of those contracts - if I hadn't kept a copy of the contract, and the company definitely hadn't kept theirs, any dispute would have been my word against theirs.