My brother-in-law has just died...the family says he has a 401K with no beneficiary.

It is possible to never name a beneficiary of a 401k plan and as a result the estate becomes the default beneficiary. Alternatively, the decedent might have named beneficiaries who have pre-deceased him. If he did not add new beneficiaries after their deaths, his estate becomes the beneficiary upon his death. The proceeds of the 401k would be distributed through the estate either in accordance with the decedent's will or the intestate act if thee is no will.

A significant aspect of having the estate named as a beneficiary might be the resulting income tax ramifications. If the estate is the beneficiary, there will be little to no continued income tax deferral for those assets. It is important to consult an accountant ASAP in this regard.