Question: For faculty lack of funding, how to find conferences that allow people to sit in without paying? For those that don't allow officially, will they check attendees' badge?

Answer: 
It depends on the conference. In recent years, the College Art Association, an annual conference for art historians and artists, has instituted a ["Pay-What-You-Wish"](https://www.collegeart.org/news/2019/02/05/pay-as-you-wish-is-back-for-caa-2019/) option. This was instituted after many adjuncts, students, and others expressed their inability to pay fees to attend an integral conference in their field. I mention this in case you are a member of an organization that holds conferences. As a member, you may be able to make your voice heard through elections and other ways that can foster a greater awareness of the high costs of attending conferences for underfunded faculty members. Hope this helps.
I would advise against crashing sessions. In my field (CS/ML/AI) organizers may be sticky about registration. I suppose that you can just try and wander in and sit down at sessions. However, you may well be asked by the organizing staff to leave if you don’t have a badge. Since the objective of attending a conference is to a great extent mingling and networking, getting thrown out will have the opposite effect.

If you have a paper/workshop paper (the latter is much easier to get accepted), then you can talk with organizers about the option of a discount which they may give depending on your circumstances. If you’re willing to volunteer they may offer a discount for example. 

As an aside, conference fees seem to be rising dramatically over the years, which I think is a serious issue.