@techuser It is not possible in oversubscribed ipo that any lot category will have single applicant but since you mention hypothetical I would like to answer with my extent of knowledge
In proportionate allotment
If HNI is 100x subscribed
So to be eligible for allotment the category should be more than 0.50(lot applied/Total oversubscription) sometime it varies but it remains near.50
so the applicant who will bid with 51 lots or more will be allotted even if he is alone in that 51 lot category but the applicant who apply 35 lots and alone will not be part of lottery and will not be allotted anything.
For 35 lots applicants to be eligible in lottery there should atleast 2 memeber(0.50>)
35÷100=0.35 (not 0.50>)
So 0.35*2=0.70
So any one out of two will be allotted.
For 10 lots applicants to be eligible in lottery
There should atleast 6 members
Because 10/100=0.10
So 0.10*6=0.60.
For this learning I give credit to Lokes ji✴️
I mentioned Hni pool category allotment to get more clarity🙏
Tech user now comming to your question in lottery
I assume there will not be allotment if there is single applicant since it will be break of the ratio that other categories may follow.if you apply 7 lots and you will be allotted then ratio will be different 1:1 and other categories may have different ratio.So it's not possible to get allotment for a single applicant.I am not sure but this what my thesis says :)
सर्वे भवन्तु सुखिनः, सर्वे सन्तु निरामयाः