Medically induced comas are routinely used in many Intensive Care Units for patients with severe brain injuries, seizures, and when mechanical ventilation is needed (e.g. in COVID19 patients).

Patients who have been placed in prolonged comas (i.e. more than a few days) frequently experience neurological damage to varying degrees. This can include memory recall and concentration problems, as well as limb-numbness and difficulties in walking / gripping etc. Some symptoms persist for months.

Prolonged medically induced coma (pMIC) is carried out routinely in intensive care medicine. pMIC leads to cognitive impairment, yet the underlying neuromorphological correlates are still unknown, as no direct studies of MIC exceeding ∼6 h on neural circuits exist.
[…]
Our findings carry profound implications for medical care, as they point out at significant structural and functional side effects of pMIC.To date,no standard approach exists to prevent cognitive side effects or alterations of brain architecture during pMIC. A better understanding of pMIC-related effects on cortical synapses, especially in the context of different widely used anesthetics,could allow for more individually tailored anesthetic regimens, and foster research on adjuvant therapeutic strategies."

Source : Proc Natl Acad Sci, US ,118(7)

Further info on MIC at Wikipedia

Editor's note: There appears to be very little published research into the subject - which is unusual given its apparently wide prevalence (see this forum as an example).

Also see: General Anaestheticsplugin-autotooltip__plain plugin-autotooltip_bigGeneral Anaesthetics

A general anaesthetic is a drug that brings about a reversible loss of consciousness.* [ see note below ]

In formal use since 1842 - the first public demonstration used Diethyl ether to carry out surgery. (Though it's likely that alcohol, another chemical classed as an anaesthetic, was previously used, extensively, for similar purposes).