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I am an international PhD student in an engineering department in US and was fully funded for all two years, but just two weeks before the fall semester (without any warning), my advisor informed me that he cannot support me, apparently he lost all the funding sources this July. He is quite happy with my research and wants me to pay this semester at least half of my tuition and live on half of the monthly stipend. He informed me that after this fall he will find a TA to support myself.

Now, my problem is that my work is experimental and needs constant funding. While TA will cover my expenses, it will not cover the experiments. Even he does not know how and when the funding for experiments will come (he didn't look confident at all). Should I think of changing the advisor now? I am personally thinking of taking an MS with my current work and looking for a funded lab for PhD in the same university.

If your advisor can't support you and your research, find another advisor as soon as possible. Your department/grad program should be able to help with this and talking to them should be your next step - it's also possible they can do something to get you funded in the immediate term. In fact, this should have been the advice your advisor gave you instead of suggesting you try to float around for a semester.

You might be able to keep your current advisor as a co-advisor or something, but frankly the way they handled this situation (waiting to tell you until now) is absolutely horrible and unprofessional (and selfish): they would have known long ago that funding was expiring and if they were waiting on some pending grant applications they needed to inform you then so you could line up other support.

I wouldn't be able to trust that person again.

Unless there is a unique situation, if your funding was coming through a grant (private or government), there is a very specific set of rules governing how that money arrives at the university and the "chain of custody". At the vast majority of universities, there is an award contract between the grantor and the grantee, administered by an office of sponsored research (or sponsored programs). That office (and very frequently the school of engineering, the specific department, and the principal investigator, in this case, probably your adviser) knows the exact terms of the contract, including end date, expected work product, equipment budget, students to be funded, etc. Usually, the money goes directly to the university, who then distributes it to the appropriate people/organizations in whatever form necessary (e.g., to a departmental account, as a tuition waiver or from the treasurer to you in the form of a paycheck). There are also university policies governing who in that chain needs to be informed of changes or updates. Your adviser is definitely one of them but you may not be.

If everything is as you described, I can only think of a single scenario in which either your adviser or the department or both did not break any internal policies by telling you so late: funding was pulled because of a major violation of the grant terms (or much less likely, something nefarious). This would be very serious however and even if it partly explained your adviser's desire to "keep this between you", the department and university have a moral obligation to explain it.

All this being said, it is absolutely in your best interest to open conversations with other potential advisers as well as the head of your department, if not the school of engineering. It is likely there are funds to be found somewhere, especially in engineering but it is not likely you can be added to some other grant before next semester, even on what they call a "no-cost extension". If there are no teaching or research assistantships, there may still be one or more department "projects" that you could work on. I wish you luck.

Either find your own source of funding or another advisor.

If you work well with your current advisor, then I would advise you to keep your current advisor and try to find funding some other way. Maybe you can apply for research stipend or scholarship or maybe some deal with your university where you can work part time teaching BSc / MSc courses at the same or neighbouring department. This is not a very uncommon solution, at least where I'm from.

Being able to work with a wise advisor who you are compatible with can be worth A LOT to you in the long run. Not only during your studies but easily as long as at least 5-10 years afterwards.