Thanks for your question.
Your daughters visa in her passport is for 6 months, correct?
Thanks for your question. I will try to help.
Provided that she leaves before her visa expires then she would not be regarded as an overstayer.
It’s perhaps not ideal that she indicated that only intends to stay for 4 months due to a job, but it’s not likely that the exit officials would know about it when she leaves the UK.
It would likely only potentially be an issue when she comes to apply for a visa in the future. It would be a really keen caseworker that spotted it, but personally if I were her I would be inclined to refer to the fact that the job offer fell through and therefore afforded her extra time to stay in the UK. I would also re-iterate in the future application that she left within the 6 months visa and was obviously able to support/accommodate herself without the need to access public funds.
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If she obtains a spouse visa then she can work in the UK without restriction..
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If she proposes to return to the UK on a visit visa then she should consider applying for a visit visa on a multi-entry basis. These can be granted for 2,5 or 10 year periods and the holder may enter the uK as many times as they like provided that they do not spend more than 6 months in any 12 month period in the UK.Tom