While I don't think this is easily possible I am wondering if it can be done. So my spool of filament had a tangle and got pulled into the printer head. Some got melted together and after cutting I have a few strands. Would it be possible to mend the ends together to make one continuous strand instead of many small strand?
Sure, but you need to be careful not to have wide or narrow spots. A fixture for this is probably better than freehand welding.
See some ideas for a homemade fuser at https://rigid.ink/blogs/news/how-to-join-or-fuse-filament-together