Getting married after ILR application is submitted

I am 28 year old Male, Indian national.

Came to UK in 2014 on student visa. Was in relationship with tier 2 work permit holder from 2013. She completed 5 year and applied for ILR 4 months back. We were planning to get married after she got ILR but my visa got curtailed recently and I have within 60 days to make fresh application or leave country. I want to know if both of us can get married while ILR application is pending. Will existing application be refused saying she has got married and she has to make fresh application or can existing application be updated by informing ukvi we are married?

What made your visa got curtailed?

Are you going to stay in the UK after being married?

I'm not sure why you believe that your partner's ILR will affected if you marry?
However, regarding your own circumstances, in order to marry in the UK as foreign nationals, you will have to register with a Home Office designated Registry Office. The Registrar is then legally bound to notify the Home Office, who can then extend the registration period from 28 to 70 days in order to interview you both separately before the wedding can go ahead.
If you have no legal status in the UK, you are obviously at risk of detention and removal. Are you in possession of your passport?
If your partner is earning a minimum of £18,600 p.a it would be wiser to marry in your own country once she has ILR and apply for a spouse settlement visa from there. Marriage in the UK won't legalise your residence and you are unable to switch to spouse from within the UK.