Design should be planned for, either as enough extra story points per story or as a separate story. And you should still have designers on your team who own and monitor the design.
The trouble is that design represents "no business value" and pure user stories will typically be dumped onto "the team" which is this blob of developers that focusses on workable software rather than maintainable software. So with the introduction of scrum, conscious design often ceases to exist. For larger, long running products this is a desaster waiting to happen of course. It will be a silent one though, development time and the number of bugs coming back will just gradually go up. And no one will regard this as worrying, we will just do more testing and feel good about it. It is not a coincidence that testing has grown into a big thing lately, also in run-off-the-mill software projects.
Fortunately, today we also have a fancy name for this: "technical debt". It is a great name because it does not sound like a problem to anyone but the development team. It implies it is their fault too, the techies should pay for it, not the business. It is their problem.
And in all fairness, it really is. The development team must make sure they do design. They are self organising and must be strong enough to reserve the resourses to do what is necessary. They commit to a planning they make themselves. There will be pressure to move ahead with features but it remains their responsibility to think things through and to have people who are responsible and accountable for this. Scrum does make it harder to maintain these basics.