Quoting from the FamilySearch Research Wiki article on Funeral Homes:
Funeral records generally began in the late Nineteenth and early Twentieth Century (1900's). Embalming within the United States was not a widely accepted practice until the Civil War and the death of President Abraham Lincoln.
Most funerals prior to the early twentieth century were a family and friends event taking place at the decedent’s home with burial taking place within twenty-four to forty-eight hours of death. Funeral homes or parlors were not used and caskets were made by the local cabinet or furniture maker.
Large cities are more likely to have earlier funeral home records. Most rural areas did not have funeral homes until the early twentieth century. Funeral directors are now responsible for initiating and filing the death certificate. Since the 1950s many funeral homes have merged with other firms or gone out of business.I have found that funeral homes or mortuaries will often preserve the records of previous business owners, so the fact that the original business no longer exists does not mean that the records have been lost. It is always a good idea to ask if any of the current business or businesses happened to keep the records from other businesses not longer in existence.
Again quoting from the Research Wiki:
The records may contain a list of the surviving immediate relatives, sometimes the names of grandchildren, in-laws, and other relatives. The record could provide residences for the listed relatives.
A copy of the obituary or notes used to prepare the obituary may be in the record, along with a record of newspapers where the obituary was placed. Records may also contain information regarding former residences, education, church affiliation, military service, membership in clubs, lodges and other organizations.
The records may include details of the grave location or type of marker. Notes regarding the funeral services, such as the officiating minister, pallbearers, and music may also be included. Information may also include life insurance information where additional genealogical information could be obtained.Additional records may also be in the form of Burial Registers, Funeral Books and Funeral Cards or programs. I have personally found all three of these types of records. In some cases, the records may be maintained with other cemetery records in a sexton's office on the cemetery itself or in another office for the cemetery in a city building or church. Often, the identity of the mortuary or funeral home is mentioned in an obituary. In many cases, finding these records may involve, not only some detective work, but undoubtedly a personal visit to the place where the ancestor died.