Singapore is not a party to major international refugee conventions, and there is no legal status for asylum seeker or refugees there. Hence, there is no public statistics provided by Singapore about asylum seekers, and it's the 1959 Immigration Act that applies to people in this kind of situation, like they were "standard" immigration candidates. So unless they are under another permanent status, asylum seekers possibly risk imprisonment, fines, and caning - no matter the merit of their claims.
This situation makes refoulement more likely, even if non-refoulement is supposed to apply to all States, including those not part of refugee conventions. According to the United Nations High Commissioner for Refugees (UNHCR):
[...] unless and until the 1951 Convention is acceded to and there is a sound legal framework for granting international protection, there are currently insufficient safeguards against refoulement. In the absence of any national asylum systems or corresponding adjudication structures in Singapore, it is likely that some asylum-seekers may have been deported or refouled upon arrival in Singapore. During 2019-2020, UNHCR has recorded three incidents where individuals were denied entry and deported without being afforded the opportunity to have their international protection needs assessed
The UNHCR also points out various problems with this situation - including increased risk of human and child trafficking.
References
Singapore: UNHCR Submission for the Universal Periodic Review - Singapore - UPR 38th Session (2021) https://www.refworld.org/pdfid/60760a114.pdf
Immigration Act 1959, sections 6(3) and 11A(6) https://sso.agc.gov.sg/Act/IA1959