Can you explain the steps to do this in a little more detail? I didn't quite follow. My list is from L4 to L27, and then when users delete names within there, I'd like the range to ignore those so when I validate another cell on another worksheet with a dropdown referencing this list, I'd like the blanks in between not to show up.

I went to Formulas > Define Name and pasted this code in (your code, but with all the A1:A100 switched to L4:L27). 

=if(row()>counta($l$4:$l$27),"",index($l$4:$l$27,small(if(isblank($l$4:$l$27),"",row($l$4:$l$27)),row())))
I called the list "Products2." Then I went to the cell where I wanted the dropdown list to show up. I went to Data Validation and selected "List" and for the list name I put =Products2. It then told me that there was an error in the formula of the list. So I'm not sure if I even did it right. Any feedback will be great, thanks!