Hi, not sure if you saw my initial query above - has her notice period now expired? Has her employment officially terminated?
Thank you. Yes you are certainly allowed to stick to the deadline you gave. Once a resignation has been submitted it is legally binding anyway – there is no option for you to reject it, although you can give the employee the opportunity to retract it if they want to, although that would be entirely on your terms. So if you gave them a specific deadline to act by and they failed to do anything about it then you may certainly say that they are now too late to change their mind and the resignation would be legally binding and their employment would terminate once their notice has come to an end.
The usual issues surrounding such circumstances are if the resignation was submitted in the heat of the moment, for example after an argument at work, but even then you are only expected to give the employee notice of a day or two to change their mind, so 2 weeks with formal notice is plenty and if they have not done anything within that time to suggest the resignation was done in error and in the heat of the moment, it would still stand. So in your case you can safely stick to the original deadline and terminate their employment once the notice period expires.