Some tar coatings become stable and weathered, but tar often does not fully cure in the same way as modern paints, epoxies, or synthetic coatings.
The word cure suggests a finished chemical transformation. That can be accurate for some modern coatings, but traditional tar behaves differently. It can lose lighter parts, oxidise, thicken, and become much less mobile, while still keeping a degree of softness or flexibility inside the coating.
This behaviour explains several familiar tar problems. A surface can look dry but soften in hot sun. An old coating can smell again when warmed. Thick deposits can remain soft long after the exposed skin has hardened. Tar is stable in use, but not always permanently fixed in the way people expect from modern finishes.
Whether this matters depends on the job. For a tarred fence, rope, shed, or traditional boat part, a slightly flexible coating may be useful. For an indoor surface, a clean painted finish, a precise joint, or a surface that people touch often, that same flexibility can be a nuisance.
So the answer is usually that tar settles rather than fully cures. It can become serviceable and long-lasting, but it may retain some ability to soften, smell, mark, or move under the right conditions.