I recently purchased a yearly subscription to PSN the other day and made a new account on my PS4, but then all my saves were on the other user. So I was wondering if I delete my online user, can I go onto my old offline user and log into PSN that way without losing the money I uploaded to my PSN account?
Yes, PSN accounts are different to ps4 accounts. You can use your PSN account on as many ps4 user accounts as you like. The ps4 user accounts only contain your game saves, so deleting a ps4 account will not delete the PSN account linked to it or it's subscription. And if your worried, just log onto the other ps4 account with your game saves with your PSN account, no need to delete the new one if your worried.
As long as both accounts are used on the same console you should be fine to use the subscription purchased for the new PSN account with you old PSN account. If you delete that new user that has the paid subscription from your console you will lose access to the PS+ subscription and any free games that were downloaded using that account.