The mefarshim on this portion of Navi (Targum, Rashi, Radak, etc.) explain that the man who died was actually Ovadiah (see Melachim Aleph 18). He was the man who kept 100 true prophets alive during their persecution by Jezebel. He hid them in 2 caves. He also provided for all of their physical needs. The cost of secretly supporting them, not only risked Ovadiah's life, but he also had to take a loan at interest to save them.
The Haftarah enters the point of the story where the lender was seeking to take away the widow's children to pay the debt which was caused by supporting the 100 prophets. Ovadiah and his wife knew they were impoverishing themselves in order to save those 100 innocents.
Here are some similarities then, between the Haftarah and Parshas VaYera:
1) There are only a few people mentioned in the Tanach who were called "G-d fearing". Abraham was called this in the parsha. Ovadiah was also called "G-d fearing" "very much". In the Haftarah, he is recognized by that label. That is how the mefarshim know who he is without his name being mentioned.
2) Ovadiah had self sacrifice for the mitzvah to keep guests as Abraham did in the Parsha. He also risked his life to protect them. This reminds us also of the actions of Lot in the Parsha who also risked his life to protect guests.
3) Abraham in the Parsha is called G-d fearing after agreeing to give his son back to Hashem. In the haftarah, Ovadiah risked the life of his two sons by impoverishing himself to save 100 lives. In both cases, Hashem did not wish to let the sons get hurt.
4) In the Parsha, the angels strike the Sodomites with blindness and close Lot's family inside behind the closed door. They ask him: "Who else do you have in the city?"
Similarly, In the Haftarah, we have words that remind us of those Parsha verses. The story in the Haftarah has Elisha tell the widow to close the door behind her with her children alone inside (so no one could see the miracle). He also asked her: "What else do you have in the house?"