Questions About Guardianship & Custody of Minors

It’s my understanding that a guardian is a person appointed to act on behalf of a minor child (or incompetent adult) during the probate process.  My questions revolve around minors who have lost both parents, and what happens to them.  Let me set the stage…

I one family, the mother died in 1889; the father, sometime between 1885-1889.  There is a probate case file for the mother, indicating her husband predeceased her and there are “no adult children.”  Furthermore, there was no land.  From what I can tell, the reason for probate was to try and settle debts against the deceased. 

So my first question is this:  Given that there was no land or significant personal property to distribute, would there have been any reason to appoint a guardian for the minor children?  If yes, what would the reason be?

Moving beyond this factor, my second question is:  Would there be some type of record (custody?) that would indicate what happened to the minor children (i.e., who was responsible for them until they came of age)?  If so, what type of record and where would it likely be found?  Does it depend on the time period?

There are at least three instances in my direct lines where both parents had died leaving minor children.  I would appreciate any help on this subject as I would like to learn more about the process and what happened to the children.  Any other ideas are also welcome.

Thanks in advance for helping me out with this :)