Finding shortest paths in undirected graphs with possibly negative edge weights
I contacted one of the authors (Kevin Wayne; thanks) of the textbook "Algorithms, 4th Edition" and got a hint:


  Try adding "t-joins" or "perfect matching" to your web searches.


Following this, I found the following two lecture notes:

Shortest Path Algorithms Luis Goddyn, Math 408: Using Edmonds' Minimum Weight Perfect Matching Algorithm to solve shortest path problems for undirected graph with negative-weight edges, provided that $(G, d)$ is conservatively weighted, that is, if $G$ has no negative weight directed circuits (circuits $C$ whose total weight $d(C)$ is negative), then Dijkstra’s algorithm stops with a shortest path tree $T$ rooted at $s$.

$T$-joins and Applications from CS 598CSC: Combinatorial Optimization uses the $T$-join techniques.