Lets say your computer failed today, you would have a file called 2018-01.wlk with data up until the last time things were downloaded but still with data in the logger and depending on the archive interval dictates how far back the logger is holding data.
You setup our new computer and all things being equal you will be able to download all the data held by the logger. So say using a 10 minute archive then you have around 17 days of data the logger can hold, download to new computer and you will get a partial 2017-12.wlk file and a 2018-01.wlk file, using the old 2017-12.wlk file assuming you have backup and the new 2018-01.wlk file then you don't have any gaps.
Say old computer failed 27th of the month then you will have a 2018-01.wlk file up until the last download, lets say up until the 26th? Download logger on new computer and you than have another 2018-01.wlk file with data only for the last 17 days (if @ 10 minute archive), so you have a 10 day data gap as you can only use 1 file, not both unless of course you could merge them, which you can with some third party software.
However if you had copied the old computer file 2018-01.wlk onto the new computer then the first download on ne computer would pick this file up and carry on without having any gaps but as you notice it is dependent and variable on the date v archive interval.