Chasm and fan "traps" are not properties of designs. They are ways of improperly using a database by blindly writing a (wrong) query based on certain properties of designs (namely constraints) rather than properly (namely the meanings of the tables). Having such properties in your design doesn't mean there's anything wrong. Of course, you still might have ill-chosen base tables.
Every base table has a corresponding predicate aka fill-in-the-[named-]blanks statement describing the application situation. The names of the blanks in the predicate are the columns of the table. A base table holds the rows that make a true statement. Every query expression combines base table names via JOIN, UNION, SELECT, EXCEPT, WHERE condition, etc and has a corresponding predicate that combines base table predicates via (respectively) AND, OR, EXISTS, AND NOT, AND condition, etc. A query result holds the rows that make a true statement.
A table and its predicate both represent an application relationship. (Aka relation. Hence the relational model, and entity-relationship modeling.) The table holds the rows that satisfy the predicate. You can't update or interpret the table without knowing the predicate. Many design methods and products do not make this all clear.
But the arrows/lines that get called "relationships" in (poor presentations of) ERM and ORM denote not application relationships but constraints. They are known limitations on what the database state can be from setting the base tables per the predicates. They have nothing to do with writing queries. (Although the limitations on base table values will naturally be reflected as limitations in query results.) So there is nothing to "resolve".
"Loops" aka cycles in these arrows/lines just reflect certain multiple-table constraints and there is nothing wrong with that per se. But arrows/lines corresponding to foreign key constraints get used by SQL DBMSs also for cascades since such a multiple-table constraint frequently requires a multiple-table update. It is cascades that must be acyclic. It just happens that some DBMSs restrict expression of constraints as a byproduct of restricting cascades. So you might have to "resolve" them to satisfy such a DBMS.
See this answer and this one.