It depends on the method. A classical knock-out implicates the disruption of the gene of interest by elimination of a part of the gene, frequently by deleting the promoter and the first exons. In this case you will have no transcription or a truncated transcript which can´t be translated.

If you use a gene silencing approach (siRNA) the mRNA is degraded and this process can be incomplete leading to a residual protein production.

It depends on the method. A classical knock-out implicates the disruption of the gene of interest by elimination of a part of the gene, frequently by deleting the promoter and the first exons. In this case you will have no transcription or a truncated transcript which can´t be translated.

If you use a gene silencing approach (siRNA) the mRNA is degraded and this process can be incomplete leading to a residual protein production.

In some cases mRNA or protein half life is an issue.

For example, you may achieve efficient mRNA silencing and stop the production of new protein, but if the protein has a long half life it may be a long period before a corresponding protein level reduction is apparent.

This is just one example.  Hope it helps

In case of complete knock-out, you thought the protein might down regulated but it didnt because that protein may be regulated by a cluster, or the effect is regulated by a signal cascade.

It depends on the turnover of protein and how rapid it gets degraded. If it has long half life, knockdown might need to be done longer to get a cleaner protein reduction. Alternatively, knockdown efficiency might be also an issue, if the efficiency is not good, residual transcripts can still be produced/amplified by other regulators, since it's not a complete knockout.