How to handle a valuable feature that is missing on 99\% of the samples in the data set?
Its best to remove such a variable. Reasons are following:

Artificial imputation can add bias and result cannot be justified because 99% data for the particular variable was artificially created.
The variables/features that you choose for building the predictive model should have low correlation with the target/outcome variable/feature. Because, variable that are highly correlated with the target/outcome variable reduces the model predictive performance.
You want a model which has low bias and low variance.