Tier-1 Dependent visa - Can dependent work? after admin review failed

HI All:

I got my ILR in September 2017 and after that I applied ILR to my wife and 3 kids - Visa expire date is 25th December 2017.
ILR rejected due to they are not in UK for 5 years continuously. So we went Admin review and it got rejected saying that Applicants are not eligible for ILR so they have to make another application with in 14 days.

Then we applied Tier-1 dependent visa in March 20 2018. as of now we did not heard any thing from home office.

My wife is working in past 1 year in a company.

Question is: between March 20 and as of now (say May 23rd) can she eligible to work in UK.
what is the condition to Work in UK.

No, she cannot work as she is now an overstayer after a refused AR process and her section 3C protection has ended.

On what date did they get their original visas and enter the UK?

2013 June .

Why did they apply for their ILR so early when they did not qualify?

Initially then were in UK Jan 2012 but they were in India for 6 months.
When I calculated from 2012 it was eligible but since 6 months out of india without visa then time resets to 0.
so again visa count started from 2013 June.

Yes, only in limited circumstances would the time out and a new visa not break the continuity of residence.

She cannot work and if her employer does the HO employee status check, they will very likely get a negative response.

She will have to wait to see if her visa is granted before she can work again.

After 2 months now if my wife resign from the company what is the impact on future ILR and impact on Tier1 dependent visa.?

If she resigns?? No impact, why would there be. She does not have to work but she is not permitted to work since AR refusal as she is an overstayer.

when we go for ILR then how we will justify these 2 months!