If no funding is available at the time of admission, what are the chances of getting funding later, and when would I find out? I applied to graduate school (masters programs) for an engineering major. It is not the most common type of engineering like electrical (my undergrad field) or mechanical. I applied to about 9 schools and heard from the 4th one today (accepted in all 4 so far). Three of these four are top 10 program (in the specific major) in US. Two of the four are top 15 graduate engineering schools in US according to published rankings.
The caveat is that all four of them have said that no funding/financial aid is available at this moment. If aid becomes available at a later date, we will notify you as soon as possible. Schools I applied to stated, if you apply before certain date you will be considered for funding and I did apply before this date. I read the post on this here and here.
What I interpreted from these two posts is that if they really like you they will offer you funding or sometimes it is offered after you accept to attend the program (does this hold any merit?). I am just slightly disappointed. It is just surprising to me that none of the school offered any funding. One of the school's professor contacted me first, after looking at my application, which I looked at as a plus (and I didn't feel like I messed up our conversation). Another school had a application deadline in January and I got positive news from them at the end of January which is unusually early (this was the most competitive university I applied to).
My question is, if they offered no funding in acceptance letter does this usually hold true or should I even consider that it might change and I might get some funding? Usually how much percent of tuition is covered with funding? Is it true that you get funding as you accept the offer?

I would not be a international student. I could be out of state, but not international. In US.
Yes it is possible, but more likely during the PhD level (it happened to three friends of mine). So basically they got the acceptance letter, they might even gave an initial fee (e.g., for first 3 months); and then, the supervisor worked out how to apply for a funding from the university or put them in a funded project.