Can a tenant to move out and break their lease without paying a fee if they can no longer live on their own due to serious medical condition?

Sorry to hear about your father's medical condition.

Unfortunately, your father will be liable for the rent for the balance of the term of the lease or until the place is re-rented.  The landlord has to mitigate (minimize) damages (the amount of monetary compensation the landlord is claiming).  If your father moves out, the landlord cannot allow the place to remain vacant for the balance of the term of the lease without making reasonable efforts to try to find another tenant.  If the landlord fails to make reasonable efforts to find another tenant, the landlord has failed to mitigate damages and the landlord's damages will be reduced accordingly.  Reasonable efforts on the part of the landlord to find another tenant will be determined by what other landlords in the area are doing to attract tenants; for example, posting a sign on the premises advertising the vacant rental or advertising in the newspaper or advertising in a local rental guide or online, etc.

Once the place is re-rented, your father's obligation to pay rent ends.  However, if the new tenant is paying less rent than your father was paying, your father would remain liable for the difference in rent for the balance of the term of his lease.  Again, the landlord has to mitigate damages by having a valid reason for charging the new tenant less rent.  Market conditions would be a valid reason for charging lower rent.