In India, in such a case we'd typically allow infinite "work from home" leave, assigning the kind of work that he could do without time crunches etc, the medical insurance for employees typically cover families too but if required we'd provide financial support above the insurance to a decent extent but not unlimited for the medical care of the daughter, and unless the guy was a massive cunt, possibly even then, his peers would voluntarily help out sometimes with babysitting or odd jobs etc if he was a single dad. This is all if it was a private business.

With poetic exaggeration -if it was a government job, the guy already has infinite leaves because our government employees just don't work anyway, unless he does something horrendous like a murder he won't be fired and he'll have free but not great medical services available.

In Latvia 9 days are payed by employer. Then you officially can have up to 26 weeks payed by government, or extended up to 52 weeks, but that needa a docotrs commision.

However, in case of a sick child it gets trickier, the official longest sick leave in one go you can have is 21 days for that (if you need to be treated at a hospital, 14 at home), all payed by the government. But you can probably just close after 21 and open a new one. You can for sure close, have one day of work and reopen, this has happened to me before.