Yes There Was
Using petrol and other substances such as Naptha (which was the key ingredient in Fels "Naptha" soap).
However the process was frought with danger and many a poor housewife,laundress and anyone else either went to their maker or suffered horrible burns. If one has access to the site where the Ironrite films are archived, there is a film about a woman who suffered horrible burns from home "dry cleaning".
Have many vintage housekeeping and laundry manuals from France, England and the United States that detail how the process was done. All advise extreme caution and that petrol was NOT to be used near any source of heat,flame or spark. It was even advised not to attempt the process if a thunderstorm was likely and or the air was charged.
Dry cleaning, as we know it was invented when a Frenchman discovered that an area of tablecloth where his maid has spilled the contents of an oil lamp,was cleaner than the surrounding textile. More important the cleaned area suffered no loss of colour or any of the other damage that can come from laundering with water.
Petrol is an excellent solvent, especially for oils, waxes and the like. However while "French Dry Cleaning" was making inroads in major cities, if one lived in the country or out on a farm, one had to make do with doing the thing at home. Also not everyone could afford to send their things out, and most every home at petrol (used in lamps, and later for engines).
Petrol fumes will eventually "air out", but one would be concerned about any residue and anyone breathing in those fumes on a regular and prolonged basis.
Oh there were all sorts of cleaning fluids and the like one could purchase, right up until the 1970's or so. Original formulas for such cleaners as "Energine", contained chemicals that would give the EPA and various others fits.