Imagine this scenario for a moment... Mitt Romney wins the nomination for the upcoming Republican presidential candidate and in order to retain the votes of the (much) more conservative members of its party, the Republicans nominate Rick Perry for the vice presidential candidate.
A few months after taking office, an assassin shoots Romney at point blank range and when apprehended, says that they did so for the Tea Party movement.
This might seem outlandish, but this situation happened in the Garfield administration with Chester Arthur serving as Vice President to retain the 'Stalwarts' in the Republican party. 100 days into office, an assassin mortally wounded Garfield and when he was wrestled to the ground, proclaimed "I am a Stalwart and Chester Arthur will be President."
This led to a very inauspicious beginning to Arthur's partial term presidency. He was elected to retain the votes of the Stalwart faction in the party. The Stalwarts wanted the United States to take a more active role in international affairs and increase they party's national appeal as well as attracting the votes of the many new immigrant groups that were coming the the United States from Ireland, Italy and elsewhere in Europe.
Garfield's faction of the Republican party still wanted to retain their old positions that they had since the civil war. Mainly retaining the "America First" attitude of isolation and anti slavery rooted views on reconstruction it had since the end of the Civil War. This faction looked at the Stalwarts with suspicion even before the assassination.
After Garfield died a few months after getting shot and Arthur took office, many of the conspiracy theories remained among the traditionalists of the Republican party throughout the rest of Garfield's life.
It's impossible to know if Arthur's adoption of many of Garfield's positions after the president's death were the result of Arthur trying to reduce suspicion of his role in Garfield's killing or if they were the honestly held views of a Gilded Age president that knew they were likely to serve only a partial term. However, Arthur's legacy will always be tied to Garfield's death.