It strongly appears that the State of Florida has in place an operation, or device, to make sure that you are arrested for driving while license suspended ("DWLS"). The scheme is as follows, 1) FL DMV suspends your license for some reason not even related to driving safety, 2) the FL DMV fails to send you the required notification letter so you are unaware that your license is suspend, 3) the FL DMV sends your suspension information to the National Driver Register ("NDR") so that if you are stopped in another state you will also be arrested, 4) you have to pay $150.00 to get the suspension lifted even if you can prove that the FL DMV suspended your license without just cause. My theory is that FL is depriving me of my 5th Amendment rights by setting in motion a chain of events that will guarantee that I am arrested if I am ever stopped thus depriving me of my freedom without due process because I was never given due process to defend against the charges.
There are two primary parts to the question. The first is, is it a violation of the due process clauses to deprive you of property or liberty without following the law: the answer is, it is. If you did not violate any law, you cannot legally be punished. That does not mean that you understand the law correctly, e.g. you may not be aware that non-payment of child support or writing rubber checks is grounds for license suspension. The second part is, can they follow a secret process where you are not informed of the charges or the results of the legal proceeding? That too is a requirement (known as procedural due process), see this article. You must be made aware that your license is subject to suspension and has been suspended. Your attorney would have to advise you, based on the details of your specific circumstance, whether your procedural due process rights had been violated. For example, if you write a rubber check, you will be ordered to appear in court (there's your notice). If you fail to show up, they can suspend your license. However, under F.S. 322.251, they do have to "notify" you that your license was suspended. The law says that
Such mailing by the department constitutes notification, and any failure by the person to receive the mailed order will not affect or stay the effective date or term of the cancellation, suspension, revocation, or disqualification of the licensee’s driving privilege.
This kind of "we sent it" definition of giving notice is probably universal in the US: no jurisdiction allows the "I never got it" defense.