When President Biden welcomes Japan’s prime minister, Fumio Kishida, to Washington this week for a visit highlighted by the pomp of a state dinner, there will be an inescapable subtext to all the ceremony: Both leaders are in a fight to keep their jobs.

With Mr. Biden facing a tight re-election contest with his predecessor and Mr. Kishida’s approval ratings falling to record lows amid a political scandal, the leaders are expected to discuss ways to entrench their countries’ alliance so it remains strong even if they are no longer around to nurture it.

The goal is to “create a situation where no one can unbind their ties,” said Narushige Michishita, a professor of international relations at the National Graduate Institute for Policy Studies in Tokyo.

The risk of drastic change appears to be much higher on the American side. Japanese officials, lawmakers and media outlets have taken to referring to “moshi Tora” — “if Trump” — or even “hobo Tora,” which roughly translates to “probably Trump,” using an abbreviation of the name of the former president and current Republican candidate.

Given Donald J. Trump’s unpredictable behavior and his transactional view of international alliances, Japanese officials are bracing for possible swings in American foreign policy.

On the Japanese side, even if Mr. Kishida does not survive a leadership election this fall in his own party, it will still control the government at least until the next general election and probably beyond that — meaning any big changes in Tokyo’s policy commitments are unlikely.