When a tenant in common dies, what happens to the tenant's interest in the estate?

It passes by probate to the deceased tenant's heirs.

Explanation:

Probate is the legal process of handing over control of properties from the name of a deceased person to the names of recipients.

It also guarantees that creditors may make reimbursement demands from the estate of the deceased, and that final tax returns are filed, including a tax return on the estate if the estate is big enough.