Python/Pandas bring value based on another DF
Use custom lambda function with generator with join for match multiple matched values, if necessary convert values to lowercase:
f = lambda x: ','.join(y for y in df2["first_name"] if x.lower() in y.lower())
df["Possiblities"] = df["Key_words"].apply(f)
print (df)
Key_words Possiblities
0 ar
1 va
2 eb
3 ne Corine
4 ke