A register status of dead, abandoned, expired or cancelled means the registration no longer gives its owner the rights a registration gives. That is a real change and it lowers your risk considerably. The checker weights dead marks at roughly a third of a live one for that reason.
It is not the same as the name being free.
What each status means
Abandoned usually means an application that was never completed: the applicant missed a deadline or did not answer the office. Expired means a registration that was not renewed. Cancelled means it was removed, sometimes because of non-use, sometimes after a dispute. On some registers the word dead covers all three.
None of these tells you whether the business behind the name still exists.
The three checks
First, is the former owner still trading under the name? Search the marketplaces and the web. A company that let a registration lapse but still sells under the name can have rights from use in the United States and several other countries, and can certainly still file a complaint.
Second, is there a newer filing? Owners re-file. So do competitors who noticed the lapse before you did. The checker shows every mark on the name, live and dead, so a new application sitting next to the dead registration is visible at a glance.
Third, is the name registered in another country you sell in? Dead in the United States, live in the EU is a common pattern for brands that consolidated. The status you see on one register says nothing about the others.
When a dead mark is a good sign
If the name has been dead for years, the former owner is gone from the market, and no one has re-filed in your class or your territories, you are looking at one of the better outcomes a search can give. Register it yourself before someone else notices.
Run the name above with your class and countries set. The results list every status, and the reasons explain why the score is what it is. A dead mark with a low score and no live neighbours is the result you want.