If you have a severely weakened immune system due to chronic lymphocytic leukemia, do vaccines even work?...and...are they safe?

Work: If the definition of work is that they produce an adequate immune response and thus render the patient safe if exposed, i would say not likely to work. Safe in general, but caution if it is a live virus.

Non-live vaccines : Are safe. A few live virus vaccines such a oral polio vaccine, nasal vaccine for flu are not suitable for a person with immune deficiency. Other vaccines may not be as effective as in a normal person but should still be taken.

Yes, and most are: Unless you have been treated (chemo, radiation, etc.), your immune system should still produce some normal-functioning cells in addition to leukemic ones. So, you can get some benefit from vaccines. Most vaccines are safe, as they are made from killed viruses and bacteria. But ones made from live viruses (varicella and oral polio, e.g.) may cause problems. See your hematologist for info.