AFAIK, the RNA doesn't get duplicated. Cells will copy a gene from the nucleus (DNA) into a segment of RNA and bring it into the body of the cell. Cells will work with this segment until it degrades. I don't the timespan for the "vaccines'" mRNA, but what I'm seeing is an average of 600 minutes in general.
Natural virus do contain genes to encode proteins to do a bunch of stuff, including reverse transcription (incorporating changes into the DNA). The "vaccines" manufacturers didn't include in their documentation any indication that such genes are present; only the spike protein code is confirmed.
edit: mRNA should be destroyed after a cell dies. If the mRNA is gets outside a cell, it could enter another cell, but naked RNA isn't stable and may degrade before being translated (into a protein). This instability is the rationale for the lipid nanoparticle used to encapsulate the RNA, to ease the delivery of the payload.
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