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: 
I have to say that I can't remember ever having my badge checked at any conference. In fact, by the second day, i've often lost my badge. What does sometimes happen is having your badge checked to get onto the campus in the first place. Also, people often have greeters at the door during registration. 

I've "sat in" on plenty conferences before when they have been happening on my campus anyway. I'm not sure I'd risk travelling to one on that basis though.
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).