You can renounce if you have not filed taxes. Here’s some general information relating to that and the relation between DoS and IRS in the context of renunciation — Pacifica
(1) Dept of State
Dept of State basically doesn’t care about one’s tax status as the citizenship itself (and the issuance of the CLN) is not dependent on one being tax compliant.
DoS’s involvement/connection with tax is the following:
(a) At the consulate the person signs DS-4081, Statement of Understanding of Consequences; one of the 12 items on it is Item 10, that renouncing “… may not exempt me from US tax income taxation [etc] …”
(b) The DS-4079, which is relevant and required for relinquishments, is not used for renunciations in Canada (or most places elsewhere AFAIK). However, some consulates may be using it for renunciation (while DoS discourages its use with renunciation, they do not forbid it, 7 FAM 1264. Your local consulate will let you know which forms they require, either on their website or when you send in an appointment request).
This questionnaire, DS-4079, asks at q. 13 (e) “Do you file US income or other tax returns?” This question is on the DS-4079 as an indicator of your ties and connections to the US, which is important if you’re claiming to have relinquished some years ago (in which case you’re trying to illustrate your lack of ties/connections/citizenship behaviour). For renunciations, it’s irrelevant if you have ties/connections/citizenship behaviour or not – and your answer has no bearing on if you can renounce or not.
(c) Dept of State is to provide IRS with a copy of each CLN they issue as per DoS Interagency Coordination and Reporting Requirements, 7 FAM 1243(a).
To log out of IRS and avoid covered expatriate status, IRS requires that the person file their exit tax form (8854), their final year form, and the five-years-previous-to-final-year forms, by June 15th of the year following the renunciation. (If you are applying for a CLN based on a relinquishing act performed prior to 4 June 2004, please read this post as the law regarding this did not come into effect until that date.)
If a person does not file, the citizenship itself remains terminated and the CLN remains valid.