Sort of. First, when we say a “substance loses its radioactivity” remember that we are talking about some radioactive element becoming a different element. That “different element” (the decay product) can also be radioactive and have a completely different half-life.
Speaking strictly in terms of one specific radioactive element, then yes, there will come a time when all atoms of that element have decayed into something else and, if its decay products are also radioactive, a time when it arrives a stable, non-radioactive element.
We just can’t ever say when that will be, which is why we have to use half-lives.
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