
absterben
to die off
The process of life functions gradually stopping, especially in plants or body parts (tissue).
Wegen der Trockenheit sterben viele Bäume im Wald ab.
Because of the drought, many trees in the forest are dying off.
to die off / go numb
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to die off
The process of life functions gradually stopping, especially in plants or body parts (tissue).
Wegen der Trockenheit sterben viele Bäume im Wald ab.
Because of the drought, many trees in the forest are dying off.

to go numb
Colloquial for the feeling when a body part becomes numb or 'falls asleep'.
Nach langem Sitzen ist mir das Bein komplett abgestorben.
After sitting for a long time, my leg had gone completely numb.

to fade away
Figuratively, the gradual disappearance of feelings or interests.
Mit der Zeit war seine anfängliche Begeisterung für das Projekt abgestorben.
Over time, his initial enthusiasm for the project had faded away.
'Absterben' (to die off / go numb) is a separable verb with the prefix 'ab-'. In a main clause, the prefix stands at the end, while in a subordinate clause it remains attached to the verb.
Wegen der Kälte sterben die Blätter an der Pflanze ab.
Because of the cold, the leaves on the plant are dying off.
The perfect tense of 'absterben' (to die off / go numb) is always formed with the auxiliary verb 'sein' (to be), because it describes a change of state. So it is 'ist abgestorben' (has died off / has gone numb).
Der alte Apfelbaum in unserem Garten ist leider letztes Jahr abgestorben.
The old apple tree in our garden unfortunately died off last year.
The exact meaning depends on the subject. With plants, it is meant literally; with body parts, it is colloquial for 'einschlafen' (to fall asleep / go numb), and with feelings it means 'verschwinden' (to disappear).
Nach dem langen Flug waren mir beide Beine abgestorben.
After the long flight, both my legs had gone numb.
When a body part 'abstirbt' (goes numb), this is a colloquial description of the feeling when it becomes numb or 'einschläft' (falls asleep / goes numb). This usage is typical of everyday speech.
Ich kann nicht aufstehen, mein Fuß ist mir abgestorben.
I can't get up; my foot has gone numb.
to die / shrink / respond
When referring to a plant, Eingehen usually means the general death of the entire organism, often because of poor conditions. Absterben, on the other hand, emphasizes the gradual loss of vital functions and can also refer to individual parts of a plant. „eingehen“ is therefore often used for the whole plant, while „absterben“ describes the ongoing process.

Bei starkem Frost können einzelne Triebe der Rose langsam absterben.
In severe frost, individual shoots of the rose may slowly die off.
Ohne genügend Wasser wird die ganze Rose eingehen.
Without enough water, the whole rose will die.