It depends on many things. The type of tax, sometimes the amount and reason for owing, and what has happened over the time.
Having heard the question too many times before, and understanding some of the misconceptions: The SOL almost never even starts to run until something that qualifies as a return has been filed. Hence, if you didn't file a return, don't even think about this defense, the statute is always open.
The SOL gets "tolled", that is time isn't counted, for many things. So, if the department can show they sent you a notice, to your last known address at the time, (makes no difference if you received it, or claim you didn't), generally the SOL is tolled until that matter is handled.
The SOL on being audited for a return is different than being assessed a tax, and audits may extend the statute, or standardly require you agree to extedn it while they do it - or they can/will issue a "jeopardy assessment"...which is absolutely allowed (almost mandatory) anytime a Govt is in jeopardy of losing the right to collect money. It is an estimated amount you owe...not surprisingly frequently a very high guess. Once an assessment is issued...by law it is considered right and you have to prove it wrong.
Experience is, even if you have a defense that it's past SOL for tax assessment...the SOL on criminal fraud may still be open...and beating the tax department on that one year....well, expect to see them again....a lot, for all types of things!