Accident death

The answer to the flat lies in your statement: "my sisters Father-in-law's name is ALSO there"

If there are multiple names, that means that there are multiple-owners. If there is some written agreement on the percentage ownership, then that will be applicable. Otherwise, it will be equal share. Of course, one can contest based upon contribution to the purchase-price but that will be complex when father-and-son are involved. So, the short answer is, both your sister and her FIL will get a share in the flat. If your sister's FIL's name is there as a co-owner, you cannot transfer the ownership of the entire flat to any person without his written consent.

As for accident claim, I presume you are referring to some form of insurance in which case the policy will clearly spell out the beneficiary's name. If for some reason that is missing, then you need to contact an advocate who specializes in insurance claims or inheritance or succession or such areas of law. DO not go to any general I-know-everything-kind-of-advocate. 

Thanks for the advice Samir for the clarification on flat matter. Accident claim I mean is the MVC. My brother in law expired in an accident caused by a truck. I heard that my sisters FIL also can claim a portion. My sister is putting all her efforts in getting all required documents so that she and her son get the claim amount. Please let me know if she can get the same.

If your sister's husband died without a will, then he is considered to have died intestate which means that all kinds of laws will become applicable about division of the estate.  His entire estate, including his share in his flat, insurance monies, bank accounts, etc. will go into the estate and from there division will take place. Normally, only the wife and child will be eligible for the share. But if it is shown that his father and other family members were dependent on him, then I think that they may also be eligible for some share in the estate. I do NOT want to misguide you here because my knowledge in this area is not clear. However, I think that I am mostly correct in my observations here.

Ask your sister to meet an advocate you specializes in succession, estate division, inheritance, etc. Best way to get one is to do a search on the Internet for some High Court opinions in your state on this issue and find the advocates involved in similar matters. Otherwise, advocates will claim expertise in every area as long as they know they are making some quick bucks...