Abortive initiation, also known as abortive transcription, is an early process of genetic transcription in which RNA polymerase binds to a DNA promoter and enters into cycles of synthesis of short mRNA transcripts which are released before the transcription complex leaves the promoter. ‘Abortive initiation’ is characterized by the repetitive synthesis of small oligomeric transcripts near the start site of transcription, and these abortive products are released from the transcribing complex without release of the polymerase or initiation factors. The abortive transcripts have the same nucleotide length as the primers employed in DNA synthesis (i.e. about 8 nucleotide bases). It appears that abortive transcripts are a fall out of evolutionary primitive RNA polymerase reaction which could do both transcription and priming of DNA replication. Abortive cycling would therefore play an important role in evolution for the emergence of the DNA world. In the DNA world, speculations are that abortive transcripts may play a role in as determinants of promoter strength, of RNA polymerase function, and a target of regulation by transcription factor GreA. Abortive transcripts may also have functional, physiologically important roles in regulating gene expression in vivo. Article Direct Detection of Abortive RNA Transcripts in Vivo

Short oligoribonucleotides (termed nanoRNAs, 2-5 nts in length) can also function as initiating substrates for RNAP, at least in bacteria. They have a huge effect on gene expression.

Mol Cell. 2011 Jun 24;42(6):817-25. doi: 10.1016/j.molcel.2011.06.005.

I will add a few more references regarding nanoRNAs:

Article A Conserved Pattern of Primer-Dependent Transcription Initia...

https://www.biorxiv.org/content/10.1101/2021.04.06.438613v1

https://pubmed.ncbi.nlm.nih.gov/22751503/

maybe cloning and identifying those abortive RNAs in a model organism first is a key step to understand the roles of such RNAs? e.g. whether there are some abortive RNAs produced from cryptic promoters? whether the abundance of abortive RNAs has correlation with corresponding gene expression, and so on. However, cloning such tiny RNAs may still be a challenge task.