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.
Open Brief
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.
It includes:
• 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)
• Storyboards
• 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)