I don't think the previous comment made "Sadly, no, if you miss a leg of a flight at any point on a ticket, they'll cancel ALL other legs of the flight." is true. I once made it very late to a flight and they rushed me through without even scanning my ticket. I don't think they meant to not scan it. I told them my name and showed them my Id and they allowed me to go through since they were just about to close the doors. It wasn't until I was sitting in the plane that I realized my ticket was not scanned. I was traveling from Hawaii to Texas which had a connecting flight in (LAX) Los Angeles.
I was worried that because my ticket was not scanned there was no record that I was even on the plane and they might cancel my entire trip. This was in April/May2018
The only thing that occurred was that I was not able to get points for flying from Hawaii to LAX, but I'm not complaining I never use those things anyways. I made it on my Los Angeles to Texas flight with no issues. Perhaps some airlines have rules against flying connection only, but the one I was on apparently lets you catch connection flights thankfully.
Maybe just check with the airlines you use to book your flights to see what their policy is because they might allow it?