According to a recent article from the New York Times, the 2014 kidnapping and murder of 43 students in Mexico may have been the result of collusion between drug Cartels and the Mexican State. The cartel involved in that specific case is named Guerreros Unidos, but the article indicates that clandestine relationships between the state and the cartels reach far back.
The article states that a major factor in the development of State-Cartel ties was the political centralization of the PRI (Institutional Revolutionary Party), the single party that controlled the Mexican state during the second half of the 20th century. According to the article, the stability of the PRI allowed for the fostering of these corrupt relationships, which largely consisted of law enforcement funneling cartel profits to the government.
When Mexico's single-party system transitioned to democracy in the late 1900s, maintaining state-cartel ties became more complex, but instability from the regime change coupled with the consolidation of drug groups into fewer, larger cartels allowed the cartels to garner a greater influence over the state, according to the New York Times.
The relationship between the Guerreros Unidos drug cartel and Mexican state agencies seems to be structured, with police personnel acting under the influence of the cartels and even updating them on law enforcement strategies, states the article. The main point is that there is a correlation between the strength of the government and that of the cartels, with the general pattern being that a weaker government makes it easier for cartels to operate. However, the article also points out that a strong government is susceptible to corruption by the cartels, as in the case of the PRI government, which is what makes the issue so complex.