I would like to point out something other answers have missed - which is how "federal work study" actually works. The world of employment in academia can be a bit unusual for those who aren't familiar with it, so I hope I can shed some light on the issue.
How Work Study Works
"Work study" money is a grant that the government provides a student such as yourself to help them gain employment experience and useful skills. However, it is also provided as a grant to schools such as your University to help defray the costs of employing students like you. Sometimes this is just free money to employ students who need to be hired anyway, and sometimes this is used to fund jobs that wouldn't otherwise be available (very volunteer-like positions that aren't strictly necessary to the institution).
Once you have worked enough to get all of your work study benefits, and thus that account is exhausted, that means that the government is no longer paying the school to employ you. That does not mean you are no longer paid!
Some "work study eligible" jobs have no budget to employ students other than work study, and so once the aid money runs out then you just can't work any more that semester due to a lack of budget. However, many jobs - especially in the sciences and IT, including lab techs and assistants especially - typically do have money to pay students above and beyond their work study, or can even employ a student who does not receive work study.
Other than asking directly, one easy way to tell the difference in the jobs is if the job listed work study as a strict requirement, or if it just said it was "work study eligible". When I worked for a nature park on my campus, that job was work study required; that meant that only students with work study could work there, and once the aid money ran out they weren't allowed to continue working. On the other hand, when working for IT they couldn't care less how much work study I received or if I had any at all - the department would foot the bill for any non-overtime hours I could manage to work (often limited to 20 hours per work while classes were in session, 40 hours over the summer and breaks).
What To Do Now
Talk with whatever person in charge you can contact. You may need to do some asking around if you can't talk with the head of the lab you had been dealing with, but there is usually a supervisor in charge of student employment for your department/school/University. While in the business world this is usually a Human Resources position, in academia it often isn't listed as such - they are just a supervisor/manager level employee working in the department or in Administration. Human Resources in Universities is usually tasked primarily with full time non-student employees - as a student employee I only ever talk with them regarding things like tax withholding and insurance, etc.
Once you've found someone you can ask, let them know you have nearly exhausted all of your work study due to increased work load from the injured professor, but also express your desire to continue working in the lab. Then just ask if you are allowed to keep working past then end of your work study budget.
They'll pay you no matter what - they are legally bound to, anyway - but you are doing them a favor of keeping them out of trouble with their bosses for going over their budget without realizing, and this is always welcomed from a student. They may indeed have a budget to pay you and you can keep working, or they might not and they will just ask you to work up until the money runs out and then stop, +/- an hour of work.
What you should not do is simply keep working without saying anything, or worse yet keep working but not filling out a time sheet. That's the kind of thing that can get people fired, as it's both illegal and a huge legal liability. If you get hurt while illegally off the clock there are a lot of people who could get into big trouble!
If they let you keep working (for pay!), great! If they don't, no one is going to blame you for quitting or anything like that. Make sure you email everyone you directly interact with to make sure they know you won't be working more due to running out of work study so they don't think you just walked off.
If you really value the experience and enjoy working at the lab, and they won't pay you, inquire of other professors or labs as to what you can do. They might have a position, or they might even have research projects you can join and get to both help at the lab and get extra items on your resume/CV! This might be volunteer (no pay), but that's a completely different thing than working at a job and effectively committing fraud by falsifying a time sheet (not filling one out properly).
Failing to ask and follow your employers (lawful) requests could cost you future work, valuable reference letters from faculty, etc. Don't do it! Ask and you'll be just fine!