If I understand what you're saying correctly, then if you are to place the pattern as one character and save it, and remove it from your inventory patterns, and then another character has the same pattern that you just saved in their inventory, the pattern will still change. The pattern does not disappear, but what happens is that whatever new pattern you put in that slot will replace the paths all over town. For example, you placed a path using your mayor, and it was in the first pattern slot in your inventory. If you save that pattern with Mabel, and then in your inventory, you replace that path pattern, with a flag or something, all of your paths will now look like that flag. It is very rare when a pattern can be used, and replaced. and whatever you used the pattern on will not change. The Custom Sign PWP is special like this. I have 3 of them in town, and I placed patterns on them, then removed the patterns from my inventory, but the signs keep the patterns. Same thing with the town flag, and some furniture I think.
Anyways, here's a TLDR. When placing paths, the path design MUST be in the inventory of whoever placed it around town, or else it will change to whatever you replace it with. The same design will not remain if you keep it on one character, and another character places it. Mabel can save designs, but because it is not in the inventory of whoever placed it, it will change.