What is the equivalent of NSLineBreakMode in iOS 7 attributed strings drawing methods?

You need to create a paragraph style.

NSMutableParagraphStyle *style = [[NSParagraphStyle defaultParagraphStyle] mutableCopy];
[style setLineBreakMode:NSLineBreakByWordWrapping];

NSDictionary *attributes = @{NSFontAttributeName: font, NSParagraphStyleAttributeName: style};
[self drawInRect:rect withAttributes:attributes];

More information here: https://developer.apple.com/documentation/uikit/nsparagraphstyle?language=objc

In Swift 5:

let style = NSMutableParagraphStyle()
style.lineBreakMode = .byWordWrapping

let attributes: [NSAttributedString.Key: Any] = [
   .font: font,
   .paragraphStyle: style
]