Échouer: The translation is stranded and used here it carries the same meaning. Like when the river dragged you several kilometers left you somewhere, avoir échoué somewhere mean that you were more or less dragged here, by people, life, ... a series of events brings you there.
An example could be, when your friend told you about this awesome trip in the countryside, and when you arrive there is only 2 almost ruined house and no phone network. Here, you can say dans quel bled paumé j'ai échoué, moi ?
Échoué can also mean that you arrived in a "bad" place/situation.
Attérir carries the same meaning as échoué, but it's more about your choice and less about the events that brought you there.
If we re-use the precedent example, it would be the trip that you decided to do, and when you arrived in this lost place without internet, you're like dans quel bled paumé j'ai attéri.
However the difference between the two is small, and you can interchange them without problem, people will still understand.
The two others have a slightly different meaning. While you can use them in the same as the other, they also have a meaning related to direction / path. (I'm not sure how to make it clear in english).
Aboutir carries the meaning that it's the end of your travel, or the end of something (like a road, a forest,...).
For example, after walking several hours in the wood, and making your way between the brambles and others plants, you suddenly arrive in a village. Here, abouti can be used.
(note: échoué can als be used here, the forest can be see as something that drag you there).
Déboucher is almost the same as abouti but is really about going out of something to arrive in a place (like exiting the forest: J'ai débouché dans ce village en sortant de la forêt).
Dans can be use aboutir, déboucher, there is no restriction:
J'ai abouti dans cette situation en suivant ce gredin
J'ai débouché dans cette allée en essayant d'échapper à la police
However déboucher is often used you arrive in front/newt to something and not inside (e.g: déboucher devant la statue de la liberté).
(note: the other word can also be used in this situation, but déboucher is often better)
However, I want to say that the meaning of these words are really (really) close in this situation, and while I tried to distinguish them and their use, you can interchanging them in most of my example and the word still perfectly mean the same.
Here is some sentence and the word you can use (without the sentence feeling strange):
- J'ai suivi cet homme dans la rue et à travers le parc et j'ai attéri/abouti dans une boite de nuit*
- J'ai voulu suivre la piste de ce renard, et après avoir traversé la rivière j'ai débouché/abouti dans une clairière.
- Je n'aurais jamais du accepter ce travail. Dans quel coin perdu j'ai échoué/attéri.
- Tu as voulu suivre les conseils de cette fille, et regarde un peu où on a attéri.
- Après la mort de ma femme, j'ai quitté mon travail. Je me suis reconverti dans l'informatique, mais mon propriétaire m'a expulsé et j'ai échoué/attéri ici.
- Si nous avions tourné à droite nous aurious débouché sur le purgatoire et si nous avions pris à gauche, nous aurions abouti/attéri/échoué en enfer. Mais en continuant tout droit à travers l'antichambre des morts, nous avons finalement abouti au Paradis.
TL;DR: you can generally interchange the 4 words together, however:
- échouer is better when you arrive somewhere and it's not good (échouer en enfer)
- atterrir works almost everytime, it should be your default choice.
- déboucher and aboutir are better when you arrive somewhere after going through something, a long road, anything.