This is javascript, everything is possible! You can attach anything to collection's constructor function, to collection's prototype, to a concrete instance of the collection. And the same is true for models.
// #1
var YourCollection = Backbone.Collection.extend({}, {sharedAttribute : 1});
var collection = new YourCollection();
console.log(collection.constructor.sharedAttribute); // 1
// #2
var YourCollection = Backbone.Collection.extend();
YourCollection.sharedAttribute = 2;
var collection = new YourCollection();
console.log(collection.constructor.sharedAttribute); // 2
// #3
var YourCollection = Backbone.Collection.extend();
YourCollection.prototype.sharedAttribute = 3;
var collection = new YourCollection();
console.log(collection.sharedAttribute); // 3
// #4
var YourCollection = Backbone.Collection.extend();
var collection = new YourCollection();
collection.sharedAttribute = 4;
console.log(collection.sharedAttribute); // 4