Normally, If the plasmid and insert cut with the same RE cane be ligated with each other. But there is another type of cloning called TA cloning which is independent of RE.

Sometimes different restriction enzymes generate the same sticky ends, and those can certainly be ligated together. Likewise, many enzymes generate blunt ends, and those can all be ligated together as well. So it is certainly possible but will depend upon what the specific enzymes as to whether it is expected or not.

This is part of traditional molecular cloning training 101. Here is a full list of enzymes with compatible cohesive ends for ligation https://www.nebiolabs.com.au/tools-and-resources/selection-charts/compatible-cohesive-ends-and-generation-of-new-restriction-sites