For half a cucumber, you should wrap the entire thing in cling film or the plastic wrap it may have been sold in.
Place it back in the container and leave in the fridge for up to one week, after which it will begin to soften and have an “undesirable texture”.
Salt will also work well for the remaining chunk of a cut cucumber.
Simply roll the fruit in a thin layer of coarse salt before placing it back in the fridge.
Thinly sliced cucumber rounds or chunks should be coated in a flavoursome dressing to keep them fresher for longer.
Balsamic vinegar, sweet honey and mustard or even a French dressing will work well here – just make sure there is an acidic ingredient to preserve the cucumber.