We have earlier seen that only 4 players have played 5 or more Tests and seen their teams winning all of them. As you may guess, the number of players who saw only defeats is somewhat higher.
In the former list, the “topper” had played in 10 Tests. Here the figure is 17 Tests, with 18 players who played in 5 or more Tests.

As you may guess, the first few are from Bangladesh (though there are none from Zimbabwe here). There are also several from other “major” Test sides including Sri Lanka, South Africa, West Indies and England.
The “topper”, Alok Kapali, was a bits-and-piece player with a top score of 85 and best of 3-3:
https://www.espncricinfo.com/bangladesh/content/player/56251.html
That 3-3 icluded Bangladesh’s first hat-trick. It also earned him a place in the trivia question “Who was the first Hindu to take a Test hat-trick?”. Note that India’s hat-tricks were by Harbhajan Singh, Irfan Pathan and more recently Jasprit Bumrah (who might be a Sikh, though this is unclear).
Next in line is the lesser-known Mohammad Sharif with 10 luckless Tests:
https://www.espncricinfo.com/bangladesh/content/player/55986.html
From England, there is JG Dewes who made his debut in the 5th Test at the Oval in 1948. He made only 1 and 10, but that would not have attracted much attention along with Bradman’s duck in his last Test.
We can extend this a little further to all those who saw defeats in 90% or more of their Tests:

Here we get 25 names. The last 7 are from Bangladesh, apart from one from Zimbabwe.
The current players here are headed by PVD Chameera (8 Tests) and DT Tiripamo (9 losses and 1 win in 10 Tests). There is still no one from India, Pakistan, Australia and New Zealand.
While India and New Zealand took a long time to register their first Test victories, they were able to draw more regularly than Bangladesh.