Yes, a corporate booking portal can keep a record of unused tickets, but how much of that value you can actually put back into a future trip depends on the airline and on the fare rules of the original ticket, not on the software.
When a traveller does not fly and the ticket is cancelled or left open instead of refunded, the value often stays with the airline for a limited period. The system can hold each of these against the right company and the right traveller, along with the airline, the original booking reference and the date by which it has to be used. That gives you one list you can look at, instead of your staff trying to remember which trips fell through last quarter and searching through old emails to find out.
The part you need to be careful about is what can be done with that value. Many airlines only allow the credit to be used by the same traveller, and usually a change fee and any difference in fare still apply. Some cheaper fares are not changeable at all, so there is nothing to recover. Where the booking came through a GDS or an airline direct connection, the ticket status normally comes back cleanly and your staff can be prompted at the point of the next booking. With some low cost carriers and consolidator fares, the credit sits in an account on the supplier side and has to be claimed there, so your portal can only carry a note and a reminder rather than apply it automatically.
It is worth asking us which of the suppliers you are connected to actually return ticket status, and in the meantime make a list of the airlines your corporate clients fly most so you know where the recoverable value really sits.