Why is 的 at the end of phrases such as 那是他们的 and 钱他们的?
他们的钱 isn't a sentence but a nominal phrase, meaning their money.
钱他们的 could be taken as the shorthand of 这钱是他们的.
那是他们的 is correct.  However 他们的是那 isn't.  You need a measure word there.  E. g.  他们的是那个。It's hard to explain why.