If you're a buyer of something and waiting on a package delivery and it arrives later than expected then nothing will happen on your end but the shipper can always ask for a refund if they wanted too.
But usually as long as you got the package delivered to your door then the shipper won't request the refund.
If you're shipping something to someone using UPS and the package is delivered late as in on a later date and it's caused by their own fault and not acts of GOD or other weather problems then you can request a refund as well.
If the package was shipped and has a guaranteed delivery time and it's a day or so late then the UPS will usually generate an automatic refund to the shipper.