This is almost always the wrong way to do things.
You cannot guarantee that this update process will run every, single day. This is Technology - stuff happens.
Updating every record is a lot of [unnecessary] work for your database to do and will, almost certainly, lock the entire table, causing other issues.
Showing stuff to Users is not the database's job.
You'll write an Application that the Users interact with and that will show them your "remaining time".
I'm sorry, but why?
Users these days want instant responses, not arbitrary and artificially-enforced delays.
If you are interested in a particular date & time, then work out when that is and store that.
You never need to change it, "in bulk" or at all,
Your application can calculate how long it is until "Real Time" catches up with it and show that duration to the User, no matter what they do in the meantime (refreshing, logging off-and-on again, etc. ), and
You can easily tell once you have reached it in a SQL query.
Keep it Simple ...
Regards,
Phill W.