[This is part of a series of defectivity case studies.]

Gorman & Yang (2019), following up on a tip from Margaret Borowczyk (p.c.) discuss inflectional gaps in Polish declension. In this language, masculine genitive singular (gen.sg.) are marked either with -a or -u. The two gen.sg. suffixes have a similar type frequency, and neither appears to be more default-like than the other. For instance, both allomorphs are used with loanwords. Because of this, it is generally agreed that the gen.sg. allomorphy is purely arbitrary and must be learned by rote, a process that continues into adulthood (e.g., Dąbrowska 2001, 2005).

Kottum (1981: 182) reports his informants have no gen.sg. for masculine-gender toponyms like Dublin ‘id.’ (e.g., *Dublina/*Dublinu), Göteborg ‘Gothenburg’ and Tarnobrzeg ‘id.’, and Gorman & Yang (2019: 184) report their informants do not have a gen.sg. for words like drut ‘wire’ (e.g., *druta/*drutu, though the latter is prescribed), rower ‘bicycle’, balon ‘baloon’, karabin ‘rifle’, autobus ‘bus’, and lotos ‘lotus flower’.

References

Dąbrowska, E. 2001. Learning a morphological system without a default: The Polish genitive. Journal of Child Language 28: 545-574.
Dąbrowska, E. 2005. Productivity and beyond: mastering the Polish genitive inflection. Journal of Child Language 32:191-205.
Gorman,. K. and Yang, C. 2019. When nobody wins. In F. Rainer, F. Gardani, H. C. Luschützky and W. U. Dressler (ed.), Competition in Inflection and Word Formation, pages 169-193. Springer.
Kottum, S. S. 1981. The genitive singular form of masculine nouns in Polish. Scando-Slavica 27: 179-186.