Body snatching is the removal of a corpse from its grave which usually required body snatchers to work in teams at night. The poor were often victims of body snatching because they did not have the means to protect the dead with guards, high cemetery walls, or metal crates over the burial sites. The stolen bodies were usually sold to medical schools for the study of anatomy. Body snatching paid a few months to several months' salary and was a huge problem during the 18th and 19th centuries due to medical reform. Medical students needed a fresh body to learn and there simply were not enough criminals dying to meet their demand for knowledge. Note that body snatching was not illegal, but the dissection of the stolen corpse was illegal and both actions were viewed as socially unacceptable due to religious and moral reasons.

Elio mentions Burke and Hare in Middlemarch when referring to Lydgate and his profession. Burke and Hare murdered at least 16 people (probably more) and sold the bodies to anatomists, Robert Knox. Burke's coconspirators made deals with the authorities and avoided punishment, but Burke was hanged and displayed before being donated to medical science. You can still see his skeleton and death mask at Surgeon's Hall in Edinburgh. 

The murders, body snatching, and public outcry lead to the Anatomy Act of 1832 which allowed for the legal donation of unclaimed bodies and personal donations of a body by the person or next of kin to medical science. This act required doctors and teachers of anatomy to obtain licenses to dissect donated cadavers, but it was not until the 1880s when embalming allowed bodies to be kept for months that ended body snatching.

Johnson, Ben. "Burke and Hare, Grave Robbers and Murderers." Historic UK, www.historic-uk.com/HistoryUK/HistoryofScotland/Burke-Hare-infamous-murd....

Levinson, David. "Body Snatching." Encyclopedia Britannica, Encyclopaedia Britannica, Inc., 11 Jan. 2019, www.britannica.com/topic/topic/body-snatching.

"Anatomy Act 1832." Wikipedia, Wikimedia Foundation, 1 July 2020, en.wikipedia.org/wiki/Anatomy_Act_1832.