To create a solid black color, a dog will have these color loci -

"A" means that the dog is solid colored and not either black & tan, saddle marked or agouti
"B" means the dog is black - "b" would be liver.
"C" means the dog is not albino, yellow, or chinchilla
"D" means the dog isn't dilute - it isn't blue or fawn.
"E" means the dog isn't masked
"g" means the dog doesn't turn grey, like Kerry Blue Terriers do
"m" means the dog is not merle
"S" means the dog is solid colored with little or no white showing
"t" means if the dog has white marks, there is no ticking in the white
For this discussion, only S and t are important.

S - In a particolored dog, one that is at least 50% white, the dog would be s(v) - piebald spotting or s(w) - extreme white. Both of these are recessive to S, so a dog that is solid color could carry for either of these. Due to the fact that the Curly gene pool is very small, if there were carriers for s(v) or s(w) out there, particolored “Curlies” should be showing up far more often than once every 20-30 years. Another reason why it is unlikely that the particolored genes have remained in the breed since the beginning is the lack of expression of “t”.

T - In a dog with white markings, if there are ticks of color in the white, it is caused by the T locus. A solid colored dog with no white could easily carry the T gene and just not be expressing it due to the fact that there are no white markings for the ticking to show in. However, solid colored dogs that are “S” can have small white marks on their chests and or toes and I have never seen any ticking in those minor white areas in a Curly. The only ticking I have seen in a Curly have been in the particolored dogs. It is more likely that the reason that ticking only shows up in particolored dogs is not because of sheer luck but because whatever breed put the particolor into the “Curly” also gave it ticking. It is far more common for particolored spaniels and pointers to have ticking than not.

How does one get a particolored “Curly”? It takes a couple of generations at least. An accidental breeding to a particolored dog to a pure for solid colored dog will produce only solid colored pups because solid (S) is dominant to particolor (sv or sw). So a mismating of a Curly to a spaniel or pointer could easily produce dogs that look like purebred Curlies, but will carry either sv or sw recessively. If one of these pups is later bred to a sibling, or grandchild who also carries the sv or sw, particolor pups will result. So people that claim that a particular particolored “Curly” couldn’t be the result of a mismating because its parents were closely watched has missed it by at least one generation. Particolored “Curlies” can be 3/4 purebred so they would look very purebred, or they could be only 1/2 purebred and show signs of crossbreeding , such as incorrect coat texture, too much coat on the legs or head, incorrect body shape, incorrect heads, etc. Since there is a wide variety of acceptable breed type, it is very easy for crossbreds to pass as Curlies as long as it more or less looks like a retriever and has a curly coat with a smooth face and legs. I have seen known Curly crossbreds that could have finished their breed Chs.

So, it is possible that the breed has carried the particolor genes in hiding for a couple of centuries, but it is far more likely that a particolored “Curly” inherited its color from a far more recent ancestor. And, simply breeding from a solid colored dog with a small white mark on the chest or toes will not result in particolored pups, nor is it an indication that such a dog carries sv or sw recessively.

Reference - The Inheritance of Coat Color in Dogs, Clarence C Little, ScD