Yes, they are out there. Ideally, you want to find a real project (external stakeholders) to work on, but if you can't there are a few sets of briefs out there on the internet. There are a few others, such as generator sites, however, they are usually not good for UX projects. A lot of these skew towards UI. Unfortunately, most of these listed and others out there focus on the end part of design and have very little user research.
• UI Projects via Briefbox (free and paid)
• Project briefs by RookieUp (pay for a set $49 USD). They are a mix of UX and UI.
• IDEO Open's Challenges by IDEO
• UX Design Mastery Blog has three projects (free)
• Product Design Challenges via Product Design Tips
• UI Design Challenges by Uplabs
• Volunteer Projects: VolunteerMatch, Catchafire, ChangeMakers.
A brief I created for my students when at GrowthX Academy is what I call an open brief. Feel free to use it as you wish to start your own project. You can end at 6 or 8 weeks depending upon your time frame.
This is an individual project. It should have all the pieces that the student has incrementally worked on as part of the human-centered design process to cohesively tell an end to end story of the product/project and describe the experience, rationale, and learnings.
• A topic to discover and create an app, website, or service. (week 1)
• Domain Research (week 1)
• A competitive analysis (week 1)
• In-Depth User Interviews (minimum of 6 User Interviews) (week 2)
• Research synthesis (affinity diagram) (week 3)
• At least 2 personas (week 3)
• Customer Journey Map (week 3)
• Concepting (week 4)
• Divergent sketches
• Sitemap (week 4)
• A minimum of 3 User Task Flows (week 4)
• Wireframes of all key screens (week 5)
• A clickable prototype (week 5)
• Usability Testing with at least 5 people from your target audience (week 6)
• Usability Testing Report (week 6)
• High-fidelity designs (week 7)
• Usability Testing with at least 5 different people from your target audience (week 8)
• Usability Testing Report (week 8)