A source/algorithm for a SUBJID value is not defined in the SDTM or other standards/regulatory documentation. It is not necessary to be a subject Screening Number. You can define it based on your need. Be creative. E.g., xxx/yyy. Where xxx is the first screening number and yyy is the second screening number. Or just xxx.
I think it’s not SDTM specific issue at all.
Agreeing with Sergiy how subject ID (SUBJID) is assigned, it's format, and business rules alike are not within the SDTM realm of issue. It is about site monitoring and screening/randomization procedures. However, do recognize the differences and importance of unique subject ID (USUBJID), which is rarely collected data on CRF. You can find such details in both CDASH and SDTM publications.
Should a re-screened patient keep the same subject ID or be assigned to a new Subject ID? What are the potential issues if the same subject ID is used?