Yes, it happens. You may have had a small leak at the compressor (seems common) and over a few months you could have lost most of your compressor oil. After that happens, the compressor can seize.
Please note that you need much more than just a new belt and compressor now. You will also have to replace the receiver/dryer (easy and cheap), the expansion valve (valve is not too expensive but the whole dash has to come out to replace it), and get the whole system correctly and completely flushed. Ford also recommends that an inline filter be installed.
You will want to skip some or all of that. If you do, the little metal particles that your dying compressor circulated in the system will kill your brand new compressor in weeks or months.