auffangen
to catch
To catch something that is falling or moving with your hands or an object before it reaches the ground.
Der Torwart konnte den Ball sicher auffangen.
The goalkeeper was able to catch the ball safely.

to catch / absorb
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to catch
To catch something that is falling or moving with your hands or an object before it reaches the ground.
Der Torwart konnte den Ball sicher auffangen.
The goalkeeper was able to catch the ball safely.

'Auffangen' (to catch / absorb) is a separable verb. The prefix 'auf' comes at the end in a main clause, while it stays attached to the verb in a subordinate clause. In the infinitive with 'zu', 'zu' goes in the middle.
Der Jongleur fängt alle Bälle geschickt auf.
The juggler skillfully catches all the balls.
The prefix 'auf-' here describes stopping or collecting something that is moving or flowing. This idea connects all the meanings: you can 'auffangen' (catch) a ball, 'auffangen' (support) a person in need, 'auffangen' (absorb) economic losses, or 'auffangen' (collect) rainwater.
Das soziale Netz soll Menschen auffangen, die ihre Arbeit verlieren.
The social safety net is meant to support people who lose their jobs.
You can recognize the exact meaning of 'auffangen' (to catch / absorb) from the object. Is it an object (ball), a person, a liquid (water), or something abstract (losses, signals)?
Kannst du das tropfende Wasser mit einem Eimer auffangen?
Can you collect the dripping water with a bucket?
In the figurative meaning, 'auffangen' (to support) always refers to a person who is being helped. The verb describes emotional or social support in a crisis.
Nach dem Tod ihres Mannes wurde sie von ihrer Familie aufgefangen.
After her husband's death, she was supported by her family.
This meaning is often used with abstract, negative nouns. Typical combinations are 'Kosten auffangen' (to absorb costs), 'Folgen auffangen' (to absorb consequences), or 'einen Rückgang auffangen' (to offset a decline).
Mit den neuen Maßnahmen will die Politik die steigenden Kosten für die Bürger auffangen.
With the new measures, policymakers want to absorb the rising costs for citizens.
When it comes to information, 'auffangen' (to pick up) often means to catch something by chance or in passing. It can refer to technical signals or to snippets of conversation.
Ich habe zufällig ein Gerücht über den neuen Chef aufgefangen.
I happened to pick up a rumor about the new boss.
to help
'helfen' and 'auffangen' can both have to do with support in a difficult situation. 'helfen' is general and fits many problems. 'auffangen' is used when, because of the help, someone or something does not completely collapse, or the consequences do not become so serious. The word often sounds stronger and describes support in a crisis, for example after a loss, an illness, or a financial problem.

Nach dem Tod ihres Mannes hat ihre Familie sie gut aufgefangen.
After her husband's death, her family supported her well.
Die Lehrerin hilft dem Schüler, weil er die Aufgabe nicht versteht.
The teacher helps the student because he does not understand the assignment.