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: 
There are a lot of reasons why conferences generally don't allow people to just wander in to sessions without notice or registration. They need some way to assure that the venue will be safe for attendees and an open door policy doesn't permit that. There are liability issues, I assume. 

If you just try it, you may get by for a while, but will probably be "caught" and escorted out, probably by police, in the US, anyway. 

But there is a "low cost option" for students at all levels. Most ACM conferences, and possibly many others, depend on student volunteers to do some of the work of running the conference, including checking badges at the doors to sessions - both large ones and small. 

Here is an example: <https://recsys.acm.org/recsys19/volunteers/>

You can look for similar things at other conferences, or just search. This was turned up by googling "Student volunteers at ACM conferences". 

Note, however, that travel and lodging are not covered. Many volunteers are from local universities, making it moot, and some students who need to travel share rooming and even car travel. Some conferences arrange sharing of hotel rooms (evidence is from other questions on this site).
I’ve never seen an official list of such conferences: who would register if it were advertised you can go for free? In addition going to a conference for the actual talks kinda misses the point: a conference is not an obligation to go to every talk, but an occasion to meet people so short of avoiding contact, the first thing people will ask is who are you, your affiliation etc and will rapidly discover you are not registered.

It is not pleasant as an organizer to see people crashing the conference: there is a real cost to organizing an event and common courtesy would be to ask the organizers for a discount or a free registration: the worse possible scenario for you is to travel somewhere and be blacklisted from the event after getting there and arranging accommodation.