Its possible yes from prior marriage, maybe one spouse co-signed for their sibling to get a FHA loan, but to have two primary residences and the occupancy issue relating from that would be the biggest issue.

For example, homeowner dies and has no spouse or children or living parents, but there are siblings.

Do you advise....Buying a sibling out, peeling wallpaper, painting, changing counter tops and appliances, new carpet, new fixtures?

One is, getting all four siblings in agreement.

Look at siblings that share the same genetics.

One of my goals with investing is to be able to teach my younger siblings & family in Atlanta to do the same. 

But the far greater returns she will likely realize not investing into real estate will replace that cost much quicker than the anticipated returns on a real estate portfolio will replace the fees associated with that asset category, and the utilization of a property management firm to manage the portfolio will come along with an average annual and ongoing cost of 10% per year...every year, where as the taxes are a one time hit.I'm advising you to consider this alternative and to engage the rest of the sibling group in a conversation with your mother as to the overall wishes, desires and individual and collective thoughts on the matter at the same time.  

We inherited/bought the property off our other siblings.

I dropped out of college, while working full time, making more than my parents as a 20 year old, bought my first house at 22 which became a rental, bought my siblings first cars, helped them through college, and have been helping my parents for a few decades.

He's championed some reform through other agencies such as getting a law passed (state I believe, doubt it was Federal) that siblings can't be separated.