Checking subset and removing extra letters

Shell Programming and Scripting
1

In each line of file, I wish to check if word1 is a non-connected subset of any of the other words in the line. If yes, keep only the words that ward1 is a subset of. Else, remove the whole line.
Also, I want to remove the letters that word1 doesn't match with, except for "_+"

Example file:

abcde  abc_+hde   ab_+ce_+de
higk    h_+al_+gk 
xyz     a_+xyz      axy_+s

Desired output:

abcde  abc_+de     ab_+c_+de
xyz     xyz
2

I do not understand what you like to do.
Post real life example with many lines, and desired output.

3

Here's a real life example, a very short snippet:
Input:

AlA$AEAt  Al_+A$AE_+At_+i  Al_+A$AE_+At_+i  Al_+<i$AE_+At_+u Al_+<i$AE_+At
AlA$AEAt Al_+<i*AE_+At_+i  Al_+<i*AE_+At_+u Al_+<i*AE_+At_+i Al_+<i*AE_+At
A*AbthA A*Ab_+at_+hA iA*Ab_+at_+a_+hA <i*Ab_+at_+i_+hA A*Ab_+at_+u_+hA

Desired output:

AlA$AEAt  Al_+A$AE_+At  Al_+A$AE_+At   
A*AbthA A*Ab_+t_+hA A*Ab_+t_+_+hA A*Ab_+t_+hA