Waiting for Cos, Tier 2 general extension after visa expire

[Lovkum]

Hello Immigration Experts,

Please kindly advice with a solution for my critical issue, I would really thank full.

I am here in UK during Oct 2013 thorough Tier 2 General and my current Visa expiry was on 07-Oct-2016.
Here the issue was during couple of week ago my present sponsor gone through UKBA renewal audit and later due to some issues my current sponsor was suspended by UKBA and not in A rated sponsor list now. So due to that they were not in a position to provide me COS for renewal.

So considering this, during last week I gone thorough few interviews and successful got an offer from one of the A rated sponsoring company based in London.

But here the issue is, the company who given me new offer had completed RLMT on 29-Sep-2016 it seems. So they informed me that they made request to UKBA for new Cos yesterday.

Here my intention is, If suppose I have received the new Cos from my new sponsor after my current valid stay had expired i.e. if suppose I received new Cos on 10th or 15th of this month then will there be any possible ways that I can apply for extension and make an successful application.

I heard about FLRO application, what was that actually. Will it be help full in my case? Please Kindly advise possible ways to make Tier 2 extension application after my current stay expire, just in case.

Thank you.