Selling them on the grey market to universities and medical schools for research and to perform educational obductions.
In England at the beginning of the 19th century there was an estimated need of 500-1000 corpses per year that could not be met by legal sources. Easy money…

Back then I think it was more that they were interested in potential jewellery the deceased would be buried with than the body itself.

Before the Anatomy Act 1832 (2 & 3 Will. 4. c. 75), the only legal supply of corpses for anatomical purposes in the UK were those condemned to death and dissection by the courts. Dissections, the main way doctors aimed to gain understanding, required fresh corpses.[6] Those who were sentenced to dissection by the courts were often guilty of capital crimes, such as murder, burglary, rape, and arson.[7] However, in 1832, Parliament of the United Kingdom passed the Anatomy Act 1832, which gave doctors and medical students the right to dissect donated bodies for education and research purposes.[8] Although this act was created to stop the illegal tradeoff of corpses, it did not provide near enough corpses needed by medical schools annually, which could be up to 500 in number.[6] This led to increased numbers of body snatching in the United Kingdom.

So probably steal corpses and pass them off as dead criminals