The leading response does a good job calling out that this is pretty risky for the traveller. Similar to skip lagging, if anything goes wrong you can end up is a pretty difficult position.
Even if you have insurance that can cover the cost of the low cost connection ticket you just missed.. try buying a new ticket at the airport for that same day or same week even and you’ve now spent more than getting a regular ticket in the first place. And that regular ticket airline is responsible for getting you to your final destination.
I did some extreme budget flying as a youth and you might just get stranded at a random airport so you better be very flexible with your plans. If it’s inside the US maybe you’re fine to rent a car or take a bus or something but if you happened to layover in UAE or something then it gets trickier
