With the default parameters STAR will only output correctly paired alignments. STAR considers two mates to be parts of the same sequence (possibly separatde by an un-sequenced portion of the insert).
The minimum alignment score and number of matches are controlled by --outFilterScoreMinOverLread and --outFilterMatchNminOverLread.
By default these parameters are equal to 0.66, i.e. if either the number of matched bases OR the alignment score (which is number of mapped bases - penalties) is < 66% of the read length (which is the sum of the lengths for both mates), the alignment will not be output and will be reported as "too short".
I generally do not recommend using un-paired alignments - in my experience, they contain a larger % of false positives.
If you want to seem them, there are several options:
1. Reduce both --outFilterScoreMinOverLread and --outFilterMatchNminOverLread to <0.5. Note, that STAR will treat the the unpaired alignments of the mates as multi-mappers.
2. Switch on "chimeric" output, which will output the unpaired alignments of two mates into Chimeric.out.sam file.
3. First map allowing for paired alignments only, output the unmapped reads, and map those as single-end reads separately for each mate.