Motivated from the fact that universal source coding on countably infinite alphabets is not feasible, the notion of almost lossless source coding is introduced. This idea -analog to the weak variable-length source coding problem proposed by Han [1]- aims at relaxing the lossless block-wise assumption to allow a distortion that vanishes asymptotically as the block-length goes to infinity1. In this setup, both feasibility and optimality results are derived for the case of memoryless sources defined on countably infinite alphabets. Our results show on one hand that Shannon entropy characterizes the minimum achievable rate (known statistics) while on the other that almost lossless universal source coding becomes feasible for the family of finite entropy stationary and memoryless sources with countably infinite alphabets.