I initially wrote this in response to a comment which was then deleted. But I think I it is sufficiently detailed to be a top-level post.

as /u/ckley said.

I think it's highly unlikely.

Sylvester magee was allegedly the last living person to have been a slave when he died in 1971. I say allegedly because this is solely based on his accounts. He had no documentation proving his birth as a slave or his participation in the civil war (or of his age as the case may be). Although not strictly historical, standard practices relating to super centenarians require some documentation of age, lest someone merely claim they were born in 1880 and say they're the oldest living person.

Eliza Moore was the last known person to have been documented to have been born a slave when she died in 1948 at the age of 105. As of the 1860's she had been documented as being the slave of a Dr. Taylor in Meigs Alabama. A text of her obituary She would have been 20 when she was emancipated.

Alfred Blackburn of North Carolina died in 1951 at the age of 108, he was allegedly the last living person in North Carolina to have been a slave, and the last person to have received a confederate pension in north Carolina. (he served as a manservant to an officer in the confederate army).

Cudjoe Lewis died in 1935 at the age of 94-95 and is believed to have been the last survivor of the transatlantic slave trade, having come to the US in 1860 on the last slave boat. Another person who was on that boat, Sally Redoshi, lived till 1937 and had been a 12 year old in 1860.

What can we draw from these examples?

In 1954-55 when Martin Luther King Junior rose to prominence in the civil rights movement and led the montgomery bus boycott. The last documented slave had died four years previously.

We can reasonably assume that there are some individuals who were born as slaves in the late 1850's up through the early 1860's and emancipated as children, and were "undocumented" as it were. But these people would have had virtually no memory of being slaves, and would have been 95-100+ at the time MLK first became a public figure.

How many are possible?

According to US Census data .08 percent of the US population is between 95-99, and .1 is 100 or older. So we can very roughly assume that even in the modern era, 1/1000 people live to be centenarians. This is the deep end of the gene pool.

In the 1860 census there were 3.9 million slaves. If we make a ridiculously generous assumption and say that 1/1000 would live to 100, that means as of 1960, the top end for surviving slaves would have been something on the order of 3900 people spread across the entire US south. really, that's way off because the 3.9 mil is ALL slaves from 0-the oldest living slave at the time, and we're looking at only a tiny percent of slaves to begin with. Realistically, it was probably hugely less than that. Dozens if not single digits.

In any case, most of these people would have had zero memory of being slaves themselves, having only been 4-5 when the civil war ended.