Company split and my part have not applied Tier-2 license

I am working in company S which was a subsidiary of company P. S has separated now but don't have their own Tier-2 sponsor license. I read the Tier-2 Guidance for Sponsors and it says that after the split the company which does not have license should apply for it within 20 working days. Otherwise the leave of the migrants will be curtailed to 60 days.

I asked my company and they said they will be applying to the license shortly. They said P had informed HO about the split and that S would be applying for license. But it has been several months and S hasn't applied.

I haven't received any letter from HO about my leave curtailment. Will everything be fine when S applies for license? Or will HO take action on S for missing the 20 working day deadline and then will curtail my leave?

I am eligible for applying to ILR. But because S does not have license I am worried that my application will be rejected. What should I do?

Just try to find another sponsor asap.

Your company is operating in total illegality. They are employing people on Tier 2 while they don't have a license. As the situation is ongoing for months, it doesn't look like they are going to do something about it soon.