Concern over identity theft seems to have risen dramatically in the Information Age, but the very concepts of identity and privacy seem to have evolved as well. Did identity thieves exist before the late 20th century, or was there basically nothing identity-wise to even steal yet?
This description of "The Will Forgeries" in 1844 Britain may go some way to answering your question.
Several members of an organized gang were convicted in this case at the Old Bailey in 1844. They identified dormant accounts in the Bank of England that contained large sums of money, then forged wills in the names of the account holders and registered fictitious deaths in the same names. Armed with the death certificates and wills, they obtained probate from the PCC at Doctor’s commons, presented the grants of probate to the Bank and collected the money.
This will was accompanied by a death certificate for Anne Slack, spinster, aged 72, of South Terrace, Pimlico, a fictitious address. The real Anne Slack was a spinster, aged about 36 in 1843, who lived at Abbots Langley with her sister and brother-in-law. She was still living there with them in 1851. It was remarkably easy to obtain a death certificate up to 1874, when the law was changed. Prior to that, no medical certification was required, so the informant’s word was enough for the registrar to issue a death certificate.